Data Pre-processing

Load needed libraries

library(fastDummies)
library(readr)
library(ggplot2)
library(dplyr)
library(caret)
library(glmnet)
library(boot)
library(tree)
library(ranger)
library(xgboost)
library(gbm)
library(vip)
library(ISLR)

Set the seed for reproducibility

set.seed(1)

Load the dataset

original_lc_data <- read.csv("LCdata.csv",sep = ";")
lc_data <- original_lc_data

remove attributes not available for prediction

lc_data <- subset(lc_data, select = -c(collection_recovery_fee, installment, issue_d,
                                       last_pymnt_amnt, last_pymnt_d, loan_status,
                                       next_pymnt_d, out_prncp, out_prncp_inv,
                                       pymnt_plan, recoveries,
                                       term, total_pymnt,
                                       total_pymnt_inv,total_rec_int, total_rec_late_fee,                                                  total_rec_prncp))
summary(lc_data)
       id             member_id          loan_amnt      funded_amnt    funded_amnt_inv    int_rate    
 Min.   :   54734   Min.   :   70473   Min.   :  500   Min.   :  500   Min.   :    0   Min.   : 5.32  
 1st Qu.: 9207230   1st Qu.:10877939   1st Qu.: 8000   1st Qu.: 8000   1st Qu.: 8000   1st Qu.: 9.99  
 Median :34433372   Median :37095300   Median :13000   Median :13000   Median :13000   Median :12.99  
 Mean   :32463636   Mean   :35000265   Mean   :14754   Mean   :14741   Mean   :14702   Mean   :13.24  
 3rd Qu.:54900100   3rd Qu.:58470266   3rd Qu.:20000   3rd Qu.:20000   3rd Qu.:20000   3rd Qu.:16.20  
 Max.   :68617057   Max.   :73544841   Max.   :35000   Max.   :35000   Max.   :35000   Max.   :28.99  
                                                                                                      
  emp_title          emp_length        home_ownership       annual_inc      verification_status     url           
 Length:798641      Length:798641      Length:798641      Min.   :      0   Length:798641       Length:798641     
 Class :character   Class :character   Class :character   1st Qu.:  45000   Class :character    Class :character  
 Mode  :character   Mode  :character   Mode  :character   Median :  65000   Mode  :character    Mode  :character  
                                                          Mean   :  75014                                         
                                                          3rd Qu.:  90000                                         
                                                          Max.   :9500000                                         
                                                          NA's   :4                                               
     desc             purpose             title             zip_code          addr_state             dti         
 Length:798641      Length:798641      Length:798641      Length:798641      Length:798641      Min.   :   0.00  
 Class :character   Class :character   Class :character   Class :character   Class :character   1st Qu.:  11.91  
 Mode  :character   Mode  :character   Mode  :character   Mode  :character   Mode  :character   Median :  17.66  
                                                                                                Mean   :  18.16  
                                                                                                3rd Qu.:  23.95  
                                                                                                Max.   :9999.00  
                                                                                                                 
  delinq_2yrs      earliest_cr_line   inq_last_6mths    mths_since_last_delinq mths_since_last_record
 Min.   : 0.0000   Length:798641      Min.   : 0.0000   Min.   :  0.0          Min.   :  0.0         
 1st Qu.: 0.0000   Class :character   1st Qu.: 0.0000   1st Qu.: 15.0          1st Qu.: 51.0         
 Median : 0.0000   Mode  :character   Median : 0.0000   Median : 31.0          Median : 70.0         
 Mean   : 0.3145                      Mean   : 0.6947   Mean   : 34.1          Mean   : 70.1         
 3rd Qu.: 0.0000                      3rd Qu.: 1.0000   3rd Qu.: 50.0          3rd Qu.: 92.0         
 Max.   :39.0000                      Max.   :33.0000   Max.   :188.0          Max.   :129.0         
 NA's   :25                           NA's   :25        NA's   :408818         NA's   :675190        
    open_acc        pub_rec          revol_bal         revol_util       total_acc      initial_list_status
 Min.   : 0.00   Min.   : 0.0000   Min.   :      0   Min.   :  0.00   Min.   :  1.00   Length:798641      
 1st Qu.: 8.00   1st Qu.: 0.0000   1st Qu.:   6443   1st Qu.: 37.70   1st Qu.: 17.00   Class :character   
 Median :11.00   Median : 0.0000   Median :  11876   Median : 56.00   Median : 24.00   Mode  :character   
 Mean   :11.55   Mean   : 0.1953   Mean   :  16930   Mean   : 55.05   Mean   : 25.27                      
 3rd Qu.:14.00   3rd Qu.: 0.0000   3rd Qu.:  20839   3rd Qu.: 73.50   3rd Qu.: 32.00                      
 Max.   :90.00   Max.   :63.0000   Max.   :2904836   Max.   :892.30   Max.   :169.00                      
 NA's   :25      NA's   :25        NA's   :2         NA's   :454      NA's   :25                          
 last_credit_pull_d collections_12_mths_ex_med mths_since_last_major_derog  policy_code application_type  
 Length:798641      Min.   : 0.00000           Min.   :  0.0               Min.   :1    Length:798641     
 Class :character   1st Qu.: 0.00000           1st Qu.: 27.0               1st Qu.:1    Class :character  
 Mode  :character   Median : 0.00000           Median : 44.0               Median :1    Mode  :character  
                    Mean   : 0.01447           Mean   : 44.1               Mean   :1                      
                    3rd Qu.: 0.00000           3rd Qu.: 61.0               3rd Qu.:1                      
                    Max.   :20.00000           Max.   :188.0               Max.   :1                      
                    NA's   :126                NA's   :599107                                             
 annual_inc_joint   dti_joint      verification_status_joint acc_now_delinq       tot_coll_amt    
 Min.   : 17950   Min.   : 3.0     Length:798641             Min.   : 0.000000   Min.   :      0  
 1st Qu.: 76167   1st Qu.:13.3     Class :character          1st Qu.: 0.000000   1st Qu.:      0  
 Median :101886   Median :17.7     Mode  :character          Median : 0.000000   Median :      0  
 Mean   :110745   Mean   :18.4                               Mean   : 0.005026   Mean   :    228  
 3rd Qu.:133000   3rd Qu.:22.6                               3rd Qu.: 0.000000   3rd Qu.:      0  
 Max.   :500000   Max.   :43.9                               Max.   :14.000000   Max.   :9152545  
 NA's   :798181   NA's   :798183                             NA's   :25          NA's   :63276    
  tot_cur_bal       open_acc_6m       open_il_6m      open_il_12m      open_il_24m     mths_since_rcnt_il
 Min.   :      0   Min.   : 0.0     Min.   : 0.0     Min.   : 0.0     Min.   : 0.0     Min.   :  0.0     
 1st Qu.:  29861   1st Qu.: 0.0     1st Qu.: 1.0     1st Qu.: 0.0     1st Qu.: 0.0     1st Qu.:  6.0     
 Median :  80647   Median : 1.0     Median : 2.0     Median : 0.0     Median : 1.0     Median : 12.0     
 Mean   : 139508   Mean   : 1.1     Mean   : 2.9     Mean   : 0.8     Mean   : 1.7     Mean   : 21.1     
 3rd Qu.: 208229   3rd Qu.: 2.0     3rd Qu.: 4.0     3rd Qu.: 1.0     3rd Qu.: 2.0     3rd Qu.: 23.0     
 Max.   :8000078   Max.   :14.0     Max.   :33.0     Max.   :12.0     Max.   :19.0     Max.   :363.0     
 NA's   :63276     NA's   :779525   NA's   :779525   NA's   :779525   NA's   :779525   NA's   :780030    
  total_bal_il       il_util        open_rv_12m      open_rv_24m       max_bal_bc        all_util     
 Min.   :     0   Min.   :  0.0    Min.   : 0.0     Min.   : 0       Min.   :    0    Min.   :  0.0   
 1st Qu.: 10164   1st Qu.: 58.4    1st Qu.: 0.0     1st Qu.: 1       1st Qu.: 2406    1st Qu.: 47.6   
 Median : 24544   Median : 74.8    Median : 1.0     Median : 2       Median : 4502    Median : 61.9   
 Mean   : 36428   Mean   : 71.5    Mean   : 1.4     Mean   : 3       Mean   : 5878    Mean   : 60.8   
 3rd Qu.: 47640   3rd Qu.: 87.7    3rd Qu.: 2.0     3rd Qu.: 4       3rd Qu.: 7774    3rd Qu.: 75.2   
 Max.   :878459   Max.   :223.3    Max.   :22.0     Max.   :43       Max.   :83047    Max.   :151.4   
 NA's   :779525   NA's   :782007   NA's   :779525   NA's   :779525   NA's   :779525   NA's   :779525  
 total_rev_hi_lim      inq_fi        total_cu_tl      inq_last_12m   
 Min.   :      0   Min.   : 0.0     Min.   : 0.0     Min.   :-4      
 1st Qu.:  13900   1st Qu.: 0.0     1st Qu.: 0.0     1st Qu.: 0      
 Median :  23700   Median : 0.0     Median : 0.0     Median : 2      
 Mean   :  32093   Mean   : 0.9     Mean   : 1.5     Mean   : 2      
 3rd Qu.:  39800   3rd Qu.: 1.0     3rd Qu.: 2.0     3rd Qu.: 3      
 Max.   :9999999   Max.   :16.0     Max.   :35.0     Max.   :32      
 NA's   :63276     NA's   :779525   NA's   :779525   NA's   :779525  

First we delete the columns which aren’t useful for our prediction

lc_data$id <- NULL
lc_data$member_id <- NULL
lc_data$zip_code <- NULL
lc_data$url <- NULL

Looks like policy_code contains just value equal to 1, it can be removed

lc_data$policy_code <- NULL

Remove additional columns which are related to the historical data

lc_data$last_credit_pull_d <- NULL

Then we delete the columns which can’t be converted to categorical and require NLP

lc_data$title <- NULL
lc_data$desc <- NULL
lc_data$emp_title <- NULL

let’s examine the loan_amnt column

sum(is.na(lc_data$loan_amnt))
[1] 0
cor(lc_data$loan_amnt, lc_data$int_rate)
[1] 0.1447189
hist(lc_data$loan_amnt, breaks = 20, main = "loan_amnt distribution", xlab = "loan_amnt", col = "lightblue", border = "black")

ggplot(data = lc_data, mapping = aes(x=int_rate,y=loan_amnt)) + geom_boxplot()

standardize loan_amnt

#lc_data$loan_amnt <- scale(lc_data$loan_amnt)

let’s examine the funded_amnt column

sum(is.na(lc_data$funded_amnt))
[1] 0
cor(lc_data$funded_amnt, lc_data$int_rate)
[1] 0.1448634
hist(lc_data$funded_amnt, breaks = 20, main = "funded_amnt distribution", xlab = "funded_amnt", col = "lightblue", border = "black")

as we can see, funded_amnt is almost the same as the loan_amnt column, consequently, we remove it.

lc_data$funded_amnt <- NULL 

let’s examine the funded_amnt_inv column

sum(is.na(lc_data$funded_amnt_inv))
[1] 0
cor(lc_data$funded_amnt_inv, lc_data$int_rate)
[1] 0.1449083
hist(lc_data$funded_amnt_inv, breaks = 20, main = "funded_amnt_inv distribution", xlab = "funded_amnt_inv", col = "lightblue", border = "black")

remove funded_amnt_inv for the same reason as above

lc_data$funded_amnt_inv <- NULL

let’s see the int_rate distribution.

hist(lc_data$int_rate, breaks = 20, main = "int_rate distribution", xlab = "int_rate", col = "lightblue", border = "black")

Standardize int rate:

#lc_data$int_rate <- scale(lc_data$int_rate)

we delete the emp_title column as there are several entries for the same job title and because there are too many different values for one-hot encoding. In addition, some titles are unclear (NLP required)

n_distinct(lc_data$emp_title)
[1] 0

As we can observe, there are 40363 NAs. We can assume 40363 do not work.

barplot(table(lc_data$emp_length),
        xlab = "emp_length years", 
        ylab = "Frequency", 
        col = "skyblue", 
        border = "black",
        cex.names = 0.6)  # The size of the main title

Since emp_length seems to be categorical, we transform it to as a factor and then as numeric. The conversion to numeric is needed for supporting the XGBoost

lc_data$emp_length <- as.factor(lc_data$emp_length)
ggplot(data = lc_data, mapping = aes(x=int_rate,y=emp_length)) + geom_boxplot()

lc_data$emp_length <- as.numeric(lc_data$emp_length)

Cleaning of home_ownership:

During the data cleaning phase, our analysis revealed that the variable “home_ownership” does not show a distinct correlation with interest rates. Specifically, among the categories, “ANY” and “OTHER” contain 2 and 154 cases, respectively, while the “NONE” category comprises 39 cases. Although the “NONE” category appears to demonstrate a higher interest rate compared to others, the limited sample size of 39 cases raises doubts about the reliability of this observation. Notably, the “NONE” category might pertain to individuals experiencing homelessness, prompting ethical concerns about loan provision to this demographic.

table(lc_data$home_ownership)

     ANY MORTGAGE     NONE    OTHER      OWN     RENT 
       2   399151       45      155    78789   320499 
ggplot(data = lc_data, mapping = aes(x=int_rate,y=home_ownership)) + geom_boxplot()

Then, we retain mortgage, own and rent:

lc_data <- lc_data %>% filter(home_ownership %in% c("MORTGAGE","OWN","RENT"))
lc_data$home_ownership <- as.numeric(as.factor(lc_data$home_ownership))

application joint handling


# merging annual income
lc_data <- lc_data %>% mutate(
    annual_inc_merged = ifelse(is.na(annual_inc_joint)== TRUE, annual_inc,annual_inc_joint)) 

lc_data <- lc_data %>% select(-annual_inc,-annual_inc_joint)


# merging debt to income ratio
lc_data <- lc_data %>% mutate(
    dti_merged = ifelse(is.na(dti_joint)== TRUE, dti,dti_joint)) 

lc_data <- lc_data %>% select(-dti,-dti_joint)

Upon reviewing the summary again, it becomes apparent that there are merely 460 joint applications, constituting a small subset within the extensive dataset of around 800k rows. Through consolidating the debt-to-income ratios (dti’s), we can pinpoint the data pertinent to our research objectives. Hence, it is advisable to eliminate the columns verification_status_joint and application_type to prevent introducing unwarranted variability into our analysis.

table(lc_data$verification_status)

   Not Verified Source Verified        Verified 
         240255          296631          261553 
table(lc_data$verification_status_joint)

                   Not Verified Source Verified        Verified 
         797979             253              53             154 
lc_data$verification_status <- as.numeric(as.factor(lc_data$verification_status))
lc_data <- lc_data %>% select(-verification_status_joint, -application_type)

Let’s checl if other is NA or a real value for purpose. It’s a real one, so we don’t have to handle it.

lc_data$purpose <- as.factor(lc_data$purpose)
ggplot(data = lc_data, mapping = aes(x=int_rate,y=purpose)) + geom_boxplot()

lc_data$purpose <- as.numeric(lc_data$purpose)

Let’s have a glance to the state address:

table(lc_data$addr_state)

    AK     AL     AR     AZ     CA     CO     CT     DC     DE     FL     GA     HI     IA     ID     IL     IN 
  1992  10101   5953  18359 116578  16934  12154   2188   2268  54819  26146   4112     13     11  31880  12393 
    KS     KY     LA     MA     MD     ME     MI     MN     MO     MS     MT     NC     ND     NE     NH     NJ 
  7105   7726   9498  18546  18906    469  20678  14306  12821   3455   2286  22135    431   1064   3865  29991 
    NM     NV     NY     OH     OK     OR     PA     RI     SC     SD     TN     TX     UT     VA     VT     WA 
  4428  11155  66790  26682   7266   9806  28221   3499   9609   1615  11618  63982   5629  23616   1606  17470 
    WI     WV     WY 
 10446   3977   1841 
lc_data$addr_state <- as.factor(lc_data$addr_state)
ggplot(data = lc_data, mapping = aes(x=int_rate,y=addr_state)) + geom_boxplot()

lc_data$addr_state <- as.numeric(lc_data$addr_state)

Regarding delinquency in the last 2 years, there are few NAs then remove them:

lc_data <- lc_data %>% 
    filter(!(is.na(delinq_2yrs)))
lc_data <- lc_data %>%
  mutate(mths_since_delinq_cat = ifelse(
    is.na(mths_since_last_delinq) == TRUE,
    "NONE",
    ifelse(
      mths_since_last_delinq <= 12,
      "Less_1_Y",
      ifelse(
        mths_since_last_delinq <= 24,
        "Less_2_Y",
        ifelse(
          mths_since_last_delinq <= 36,
          "Less_3_Y",
          ifelse(mths_since_last_delinq <= 48, "Less_4_Y", "More_4_Y")
        )
      )
    )
  )) %>% select(-mths_since_last_delinq)
          
lc_data$mths_since_delinq_cat <- as.factor(lc_data$mths_since_delinq_cat)
ggplot(data = lc_data, mapping = aes(x=int_rate,y=mths_since_delinq_cat))+geom_boxplot()

lc_data$mths_since_delinq_cat <- as.numeric(lc_data$mths_since_delinq_cat)
lc_data <- lc_data %>%
  mutate(mths_since_last_record_cat = ifelse(
    is.na(mths_since_last_record) == TRUE,
    "NONE",
    ifelse(
      mths_since_last_record <= 12,
      "Less_1_Y",
      ifelse(
        mths_since_last_record <= 24,
        "Less_2_Y",
        ifelse(
          mths_since_last_record <= 36,
          "Less_3_Y",
          ifelse(mths_since_last_record <= 48, "Less_4_Y", "More_4_Y")
        )
      )
    )
  )) %>% select(-mths_since_last_record)

lc_data$mths_since_last_record_cat <- as.factor(lc_data$mths_since_last_record_cat)
ggplot(data = lc_data, mapping = aes(x=int_rate,y=mths_since_last_record_cat))+geom_boxplot()

lc_data$mths_since_last_record_cat <- as.numeric(lc_data$mths_since_last_record_cat)
lc_data <-lc_data %>% 
  mutate(mths_since_last_major_derog_cat =  ifelse(
    is.na(mths_since_last_major_derog) == TRUE,
    "NONE",
    ifelse(
      mths_since_last_major_derog <= 12,
      "Less_1_Y",
      ifelse(
        mths_since_last_major_derog <= 24,
        "Less_2_Y",
        ifelse(
          mths_since_last_major_derog <= 36,
          "Less_3_Y",
          ifelse(mths_since_last_major_derog <= 48, "Less_4_Y", "More_4_Y")
        )
      )
    )
  )) %>% select(-mths_since_last_major_derog)

lc_data$mths_since_last_major_derog_cat <- as.factor(lc_data$mths_since_last_major_derog_cat)
ggplot(data = lc_data, mapping = aes(x=int_rate,y=mths_since_last_major_derog_cat))+geom_boxplot()

lc_data$mths_since_last_major_derog_cat <- as.numeric(lc_data$mths_since_last_major_derog_cat)
lc_data$initial_list_status <- as.factor(lc_data$initial_list_status)
ggplot(data = lc_data, mapping = aes(x=int_rate,y=initial_list_status))+geom_boxplot()

lc_data$initial_list_status <- as.numeric(lc_data$initial_list_status)

Let’s check which columns still have null values

colSums(is.na(lc_data))
                      loan_amnt                        int_rate                      emp_length 
                              0                               0                               0 
                 home_ownership             verification_status                         purpose 
                              0                               0                               0 
                     addr_state                     delinq_2yrs                earliest_cr_line 
                              0                               0                               0 
                 inq_last_6mths                        open_acc                         pub_rec 
                              0                               0                               0 
                      revol_bal                      revol_util                       total_acc 
                              2                             428                               0 
            initial_list_status      collections_12_mths_ex_med                  acc_now_delinq 
                              0                              99                               0 
                   tot_coll_amt                     tot_cur_bal                     open_acc_6m 
                          63132                           63132                          779302 
                     open_il_6m                     open_il_12m                     open_il_24m 
                         779302                          779302                          779302 
             mths_since_rcnt_il                    total_bal_il                         il_util 
                         779807                          779302                          781784 
                    open_rv_12m                     open_rv_24m                      max_bal_bc 
                         779302                          779302                          779302 
                       all_util                total_rev_hi_lim                          inq_fi 
                         779302                           63132                          779302 
                    total_cu_tl                    inq_last_12m               annual_inc_merged 
                         779302                          779302                               0 
                     dti_merged           mths_since_delinq_cat      mths_since_last_record_cat 
                              0                               0                               0 
mths_since_last_major_derog_cat 
                              0 

The columns revol_bal and revol_util contain only few NA values, those values can’t be replaced with 0, then we filter the values which are not NA

lc_data <- lc_data %>% 
    filter(!(is.na(revol_bal))) %>% 
        filter(!(is.na(revol_util)))

Let’s check which columns still have null values

names(which(colSums(is.na(lc_data)) > 0))
 [1] "collections_12_mths_ex_med" "tot_coll_amt"               "tot_cur_bal"               
 [4] "open_acc_6m"                "open_il_6m"                 "open_il_12m"               
 [7] "open_il_24m"                "mths_since_rcnt_il"         "total_bal_il"              
[10] "il_util"                    "open_rv_12m"                "open_rv_24m"               
[13] "max_bal_bc"                 "all_util"                   "total_rev_hi_lim"          
[16] "inq_fi"                     "total_cu_tl"                "inq_last_12m"              

Replace null values with 0 where is possible

lc_data <-
  lc_data %>%
  mutate(open_acc_6m = ifelse(is.na(open_acc_6m) == TRUE, 0, open_acc_6m)) %>%
  mutate(tot_cur_bal = ifelse(is.na(tot_cur_bal) == TRUE, 0, tot_cur_bal)) %>%
  mutate(open_il_6m = ifelse(is.na(open_il_6m) == TRUE, 0, open_il_6m)) %>%
  mutate(open_il_12m = ifelse(is.na(open_il_12m) == TRUE, 0, open_il_12m)) %>%
  mutate(open_il_24m = ifelse(is.na(open_il_24m) == TRUE, 0, open_il_24m)) %>%
  mutate(mths_since_rcnt_il = ifelse(is.na(mths_since_rcnt_il) == TRUE, 0, mths_since_rcnt_il)) %>%
  mutate(total_bal_il = ifelse(is.na(total_bal_il) == TRUE, 0, total_bal_il)) %>%
  mutate(il_util = ifelse(is.na(il_util) == TRUE, 0, il_util)) %>%
  mutate(open_rv_12m = ifelse(is.na(open_rv_12m) == TRUE, 0, open_rv_12m)) %>%
  mutate(total_rev_hi_lim = ifelse(is.na(total_rev_hi_lim) == TRUE, 0, total_rev_hi_lim)) %>%
  mutate(max_bal_bc = ifelse(is.na(max_bal_bc) == TRUE, 0, max_bal_bc)) %>%
  mutate(all_util = ifelse(is.na(all_util) == TRUE, 0, all_util)) %>%
  mutate(inq_fi = ifelse(is.na(inq_fi) == TRUE, 0, inq_fi)) %>%
  mutate(total_cu_tl = ifelse(is.na(total_cu_tl) == TRUE, 0, total_cu_tl)) %>%
  mutate(inq_last_12m = ifelse(is.na(inq_last_12m) == TRUE, 0, inq_last_12m)) %>%
  mutate(open_rv_24m = ifelse(is.na(open_rv_24m) == TRUE, 0, open_rv_24m)) %>%
  mutate(tot_coll_amt = ifelse(is.na(tot_coll_amt)== TRUE,0, tot_coll_amt)) %>%
  mutate(collections_12_mths_ex_med = ifelse(is.na(collections_12_mths_ex_med)== TRUE,0, collections_12_mths_ex_med))

earliest_cr_line contains the month the borrower’s earliest reported credit line was opened. Even if this date consists only on month and year, still there are too many unique values. We could transform the dates in to a numerical value, by converting them from date into Unix Time. This unit measures time by the number of seconds that have elapsed since 00:00:00 UTC on 1 January 1970. Since this column doesn’t contain the day number, we take as a reference the first day of the month.

lc_data <- lc_data %>% 
    filter(!(is.na(earliest_cr_line)))

# function to replace dates with unix time
to_unix_time <- function(date) {
  tmp <- paste("01", date, sep="-")
  return (as.numeric(as.POSIXct(tmp, format="%d-%b-%Y", tz="UTC")))
}

# map dates to unix time
lc_data$earliest_cr_line <- apply(lc_data, 1, function(row) to_unix_time(row["earliest_cr_line"]))

# standardize them
#lc_data$earliest_cr_line <- scale(lc_data$earliest_cr_line)
summary(lc_data)
   loan_amnt        int_rate       emp_length    home_ownership  verification_status    purpose      
 Min.   :  500   Min.   : 5.32   Min.   : 1.00   Min.   :1.000   Min.   :1.000       Min.   : 1.000  
 1st Qu.: 8000   1st Qu.: 9.99   1st Qu.: 3.00   1st Qu.:1.000   1st Qu.:1.000       1st Qu.: 3.000  
 Median :13000   Median :12.99   Median : 4.00   Median :2.000   Median :2.000       Median : 3.000  
 Mean   :14757   Mean   :13.24   Mean   : 5.11   Mean   :1.901   Mean   :2.027       Mean   : 3.571  
 3rd Qu.:20000   3rd Qu.:16.20   3rd Qu.: 7.00   3rd Qu.:3.000   3rd Qu.:3.000       3rd Qu.: 3.000  
 Max.   :35000   Max.   :28.99   Max.   :12.00   Max.   :3.000   Max.   :3.000       Max.   :14.000  
   addr_state     delinq_2yrs      earliest_cr_line     inq_last_6mths       open_acc        pub_rec       
 Min.   : 1.00   Min.   : 0.0000   Min.   :-820540800   Min.   : 0.0000   Min.   : 1.00   Min.   : 0.0000  
 1st Qu.:10.00   1st Qu.: 0.0000   1st Qu.: 770428800   1st Qu.: 0.0000   1st Qu.: 8.00   1st Qu.: 0.0000  
 Median :24.00   Median : 0.0000   Median : 936144000   Median : 0.0000   Median :11.00   Median : 0.0000  
 Mean   :24.14   Mean   : 0.3143   Mean   : 889273164   Mean   : 0.6947   Mean   :11.55   Mean   : 0.1954  
 3rd Qu.:37.00   3rd Qu.: 0.0000   3rd Qu.:1051747200   3rd Qu.: 1.0000   3rd Qu.:14.00   3rd Qu.: 0.0000  
 Max.   :51.00   Max.   :39.0000   Max.   :1351728000   Max.   :33.0000   Max.   :90.00   Max.   :63.0000  
   revol_bal         revol_util       total_acc      initial_list_status collections_12_mths_ex_med
 Min.   :      0   Min.   :  0.00   Min.   :  1.00   Min.   :1.000       Min.   : 0.00000          
 1st Qu.:   6450   1st Qu.: 37.70   1st Qu.: 17.00   1st Qu.:1.000       1st Qu.: 0.00000          
 Median :  11881   Median : 56.00   Median : 24.00   Median :1.000       Median : 0.00000          
 Mean   :  16934   Mean   : 55.05   Mean   : 25.27   Mean   :1.485       Mean   : 0.01448          
 3rd Qu.:  20844   3rd Qu.: 73.50   3rd Qu.: 32.00   3rd Qu.:2.000       3rd Qu.: 0.00000          
 Max.   :2904836   Max.   :892.30   Max.   :169.00   Max.   :2.000       Max.   :20.00000          
 acc_now_delinq       tot_coll_amt      tot_cur_bal       open_acc_6m         open_il_6m        open_il_12m      
 Min.   : 0.000000   Min.   :      0   Min.   :      0   Min.   : 0.00000   Min.   : 0.00000   Min.   : 0.00000  
 1st Qu.: 0.000000   1st Qu.:      0   1st Qu.:  23195   1st Qu.: 0.00000   1st Qu.: 0.00000   1st Qu.: 0.00000  
 Median : 0.000000   Median :      0   Median :  65402   Median : 0.00000   Median : 0.00000   Median : 0.00000  
 Mean   : 0.005026   Mean   :    210   Mean   : 128461   Mean   : 0.02641   Mean   : 0.06982   Mean   : 0.01816  
 3rd Qu.: 0.000000   3rd Qu.:      0   3rd Qu.: 195864   3rd Qu.: 0.00000   3rd Qu.: 0.00000   3rd Qu.: 0.00000  
 Max.   :14.000000   Max.   :9152545   Max.   :8000078   Max.   :14.00000   Max.   :33.00000   Max.   :12.00000  
  open_il_24m       mths_since_rcnt_il  total_bal_il       il_util         open_rv_12m        open_rv_24m      
 Min.   : 0.00000   Min.   :  0.0000   Min.   :     0   Min.   :  0.000   Min.   : 0.00000   Min.   : 0.00000  
 1st Qu.: 0.00000   1st Qu.:  0.0000   1st Qu.:     0   1st Qu.:  0.000   1st Qu.: 0.00000   1st Qu.: 0.00000  
 Median : 0.00000   Median :  0.0000   Median :     0   Median :  0.000   Median : 0.00000   Median : 0.00000  
 Mean   : 0.03991   Mean   :  0.4918   Mean   :   872   Mean   :  1.489   Mean   : 0.03316   Mean   : 0.07114  
 3rd Qu.: 0.00000   3rd Qu.:  0.0000   3rd Qu.:     0   3rd Qu.:  0.000   3rd Qu.: 0.00000   3rd Qu.: 0.00000  
 Max.   :19.00000   Max.   :363.0000   Max.   :878459   Max.   :223.300   Max.   :22.00000   Max.   :43.00000  
   max_bal_bc         all_util       total_rev_hi_lim      inq_fi          total_cu_tl        inq_last_12m     
 Min.   :    0.0   Min.   :  0.000   Min.   :      0   Min.   : 0.00000   Min.   : 0.00000   Min.   :-4.00000  
 1st Qu.:    0.0   1st Qu.:  0.000   1st Qu.:  11700   1st Qu.: 0.00000   1st Qu.: 0.00000   1st Qu.: 0.00000  
 Median :    0.0   Median :  0.000   Median :  21800   Median : 0.00000   Median : 0.00000   Median : 0.00000  
 Mean   :  140.8   Mean   :  1.456   Mean   :  29564   Mean   : 0.02262   Mean   : 0.03668   Mean   : 0.04733  
 3rd Qu.:    0.0   3rd Qu.:  0.000   3rd Qu.:  37900   3rd Qu.: 0.00000   3rd Qu.: 0.00000   3rd Qu.: 0.00000  
 Max.   :83047.0   Max.   :151.400   Max.   :9999999   Max.   :16.00000   Max.   :35.00000   Max.   :32.00000  
 annual_inc_merged   dti_merged    mths_since_delinq_cat mths_since_last_record_cat mths_since_last_major_derog_cat
 Min.   :   1896   Min.   : 0.00   Min.   :1.000         Min.   :1.000              Min.   :1.000                  
 1st Qu.:  45000   1st Qu.:11.91   1st Qu.:3.000         1st Qu.:6.000              1st Qu.:6.000                  
 Median :  65000   Median :17.66   Median :6.000         Median :6.000              Median :6.000                  
 Mean   :  75038   Mean   :18.13   Mean   :4.576         Mean   :5.779              Mean   :5.435                  
 3rd Qu.:  90000   3rd Qu.:23.94   3rd Qu.:6.000         3rd Qu.:6.000              3rd Qu.:6.000                  
 Max.   :9500000   Max.   :43.86   Max.   :6.000         Max.   :6.000              Max.   :6.000                  
#round(cor(lc_data),2)

# TODO: (parte vecchia), split 80/20 e linear regression...
# Create indices for splitting (80% train, 20% test)
train_indices <- createDataPartition(lc_data$int_rate, p = 0.8, list = FALSE)

# Create training and testing datasets
train_data <- lc_data[train_indices, ]
test_data <- lc_data[-train_indices, ]

#### Linear Regression ####
#lm.fit <- lm(int_rate ~ ., data = train_data)

# TODO: check collinearity and multicollinearity
#vif(lm.fit) # there is multicollinearity
#cor(lc_data) 

# Make predictions on training and testing data
#train_predictions <- predict(lm.fit, newdata = train_data)
#test_predictions <- predict(lm.fit, newdata = test_data)

# Evaluate model performance on training data
#train_rmse <- sqrt(mean((train_predictions - train_data$int_rate)^2))
#train_r_squared <- summary(lm.fit)$r.squared

# Evaluate model performance on testing data
#test_rmse <- sqrt(mean((test_predictions - test_data$int_rate)^2))
#test_r_squared <- summary(lm.fit, test_data)$r.squared

# Print evaluation metrics
#cat("Training RMSE:", train_rmse, "\n")
#cat("Training R-squared:", train_r_squared, "\n")
#rmse <- sqrt(mean(lm.fit$residuals^2))
#print(rmse)
# 1% of the total rows
sample_train_size <- floor(0.01 * nrow(train_data))
sample_test_size <- floor(0.01 * nrow(test_data))

# Randomly select 1% of the rows
sampled_train_data <- train_data[sample(nrow(train_data), size = sample_train_size, replace = FALSE), ]
sampled_test_data <- test_data[sample(nrow(test_data), size = sample_test_size, replace = FALSE), ]

sampled_train_data <- train_data
sampled_test_data <- test_data

#### Linear Regression ####

lm.fit <- lm(int_rate ~ ., data = sampled_train_data)

# Make predictions on the training and testing data
lm.train_predictions <- predict(lm.fit, newdata = sampled_train_data)
lm.test_predictions <- predict(lm.fit, newdata = sampled_test_data)

# Calculate Mean Squared Error (MSE) for training and testing
lm.train_mse <- mean((lm.train_predictions - sampled_train_data$int_rate)^2)
lm.test_mse <- mean((lm.test_predictions - sampled_test_data$int_rate)^2)

# Calculate Root Mean Squared Error (RMSE) for training and testing
lm.train_rmse <- sqrt(lm.train_mse)
lm.test_rmse <- sqrt(lm.test_mse)

# Calculate Mean Absolute Error (MAE) for training and testing
lm.train_mae <- mean(abs(lm.train_predictions - sampled_train_data$int_rate))
lm.test_mae <- mean(abs(lm.test_predictions - sampled_test_data$int_rate))

# Calculate R-squared (R²) for training and testing
lm.train_r2 <- 1 - (sum((sampled_train_data$int_rate - lm.train_predictions)^2) / sum((sampled_train_data$int_rate - mean(sampled_train_data$int_rate))^2))
lm.test_r2 <- 1 - (sum((sampled_test_data$int_rate - lm.test_predictions)^2) / sum((sampled_test_data$int_rate - mean(sampled_test_data$int_rate))^2))

# Display the metrics
cat("Training MSE:", lm.train_mse, "\n")
Training MSE: 13.26248 
cat("Testing MSE:", lm.test_mse, "\n")
Testing MSE: 13.6664 
cat("Training RMSE:", lm.train_rmse, "\n")
Training RMSE: 3.641768 
cat("Testing RMSE:", lm.test_rmse, "\n")
Testing RMSE: 3.696809 
cat("Training MAE:", lm.train_mae, "\n")
Training MAE: 2.885102 
cat("Testing MAE:", lm.test_mae, "\n")
Testing MAE: 2.889154 
cat("Training R-squared (R²):", lm.train_r2, "\n")
Training R-squared (R²): 0.3094189 
cat("Testing R-squared (R²):", lm.test_r2, "\n")
Testing R-squared (R²): 0.2880591 
#### Linear Regresion applying Cross Validation with k=2 to k=10  ####


# Assuming 'sampled_train_data' is your training data set

# Initialize lists to store models and their results
models <- list()
results <- data.frame()

# Define the number of folds for cross-validation
num_folds <- 10
folds <- createFolds(sampled_train_data$int_rate, k = num_folds, list = TRUE)

# Perform k-fold cross-validation
for(i in seq_along(folds)) {
  # Split the data into training and testing for the current fold
  train_indices <- folds[[i]]
  test_indices <- setdiff(seq_len(nrow(sampled_train_data)), train_indices)
  
  train_data_fold <- sampled_train_data[train_indices, ]
  test_data_fold <- sampled_train_data[test_indices, ]
  
  # Fit the model on the training fold
  lm_model <- lm(int_rate ~ ., data = train_data_fold)
  models[[i]] <- lm_model  # Store the model
  
  # Make predictions on the training and testing fold
  train_predictions <- predict(lm_model, newdata = train_data_fold)
  test_predictions <- predict(lm_model, newdata = test_data_fold)
  
  # Calculate metrics for training fold
  train_mse <- mean((train_predictions - train_data_fold$int_rate)^2)
  train_rmse <- sqrt(train_mse)
  train_mae <- mean(abs(train_predictions - train_data_fold$int_rate))
  train_r2 <- summary(lm_model)$r.squared
  
  # Calculate metrics for testing fold
  test_mse <- mean((test_predictions - test_data_fold$int_rate)^2)
  test_rmse <- sqrt(test_mse)
  test_mae <- mean(abs(test_predictions - test_data_fold$int_rate))
  test_r2 <- 1 - (sum((test_data_fold$int_rate - test_predictions)^2) / sum((test_data_fold$int_rate - mean(test_data_fold$int_rate))^2))
  
  # Store metrics in the results dataframe
  results <- rbind(results, data.frame(
    Fold = i,
    Train_MSE = train_mse, Test_MSE = test_mse,
    Train_RMSE = train_rmse, Test_RMSE = test_rmse,
    Train_MAE = train_mae, Test_MAE = test_mae,
    Train_R2 = train_r2, Test_R2 = test_r2
  ))
}

# Display the models and their metrics
print(models)
[[1]]

Call:
lm(formula = int_rate ~ ., data = train_data_fold)

Coefficients:
                    (Intercept)                        loan_amnt                       emp_length  
                      6.335e+00                        1.261e-04                        1.064e-02  
                 home_ownership              verification_status                          purpose  
                      1.931e-01                        8.601e-01                        3.559e-01  
                     addr_state                      delinq_2yrs                 earliest_cr_line  
                      2.676e-03                        4.429e-02                        2.146e-09  
                 inq_last_6mths                         open_acc                          pub_rec  
                      9.875e-01                        6.126e-02                        4.337e-01  
                      revol_bal                       revol_util                        total_acc  
                      8.094e-06                        4.396e-02                       -3.199e-02  
            initial_list_status       collections_12_mths_ex_med                   acc_now_delinq  
                     -6.185e-01                        2.261e-01                        1.500e+00  
                   tot_coll_amt                      tot_cur_bal                      open_acc_6m  
                      2.307e-05                       -1.057e-06                       -1.049e-01  
                     open_il_6m                      open_il_12m                      open_il_24m  
                     -1.773e-01                        6.202e-01                        8.539e-02  
             mths_since_rcnt_il                     total_bal_il                          il_util  
                     -7.375e-03                        1.206e-06                       -1.392e-04  
                    open_rv_12m                      open_rv_24m                       max_bal_bc  
                      2.434e-01                        4.545e-03                       -4.965e-05  
                       all_util                 total_rev_hi_lim                           inq_fi  
                     -6.684e-03                       -2.158e-05                        4.006e-02  
                    total_cu_tl                     inq_last_12m                annual_inc_merged  
                     -5.500e-02                        6.120e-02                       -7.378e-06  
                     dti_merged            mths_since_delinq_cat       mths_since_last_record_cat  
                      6.407e-02                       -1.807e-01                       -1.394e-01  
mths_since_last_major_derog_cat  
                     -1.629e-01  


[[2]]

Call:
lm(formula = int_rate ~ ., data = train_data_fold)

Coefficients:
                    (Intercept)                        loan_amnt                       emp_length  
                      6.495e+00                        1.238e-04                        2.940e-03  
                 home_ownership              verification_status                          purpose  
                      1.369e-01                        8.660e-01                        3.471e-01  
                     addr_state                      delinq_2yrs                 earliest_cr_line  
                      1.515e-03                        1.398e-02                        2.024e-09  
                 inq_last_6mths                         open_acc                          pub_rec  
                      1.008e+00                        6.684e-02                        3.921e-01  
                      revol_bal                       revol_util                        total_acc  
                      4.134e-06                        4.416e-02                       -3.255e-02  
            initial_list_status       collections_12_mths_ex_med                   acc_now_delinq  
                     -6.204e-01                        3.396e-01                        1.791e+00  
                   tot_coll_amt                      tot_cur_bal                      open_acc_6m  
                      1.774e-05                       -1.541e-06                        1.707e-01  
                     open_il_6m                      open_il_12m                      open_il_24m  
                     -2.146e-01                        6.587e-01                       -1.285e-01  
             mths_since_rcnt_il                     total_bal_il                          il_util  
                     -9.629e-03                        4.188e-06                       -7.130e-03  
                    open_rv_12m                      open_rv_24m                       max_bal_bc  
                      5.293e-02                        1.003e-01                       -1.012e-04  
                       all_util                 total_rev_hi_lim                           inq_fi  
                      6.933e-03                       -2.038e-05                        1.058e-03  
                    total_cu_tl                     inq_last_12m                annual_inc_merged  
                     -7.185e-02                        5.545e-02                       -4.952e-06  
                     dti_merged            mths_since_delinq_cat       mths_since_last_record_cat  
                      7.052e-02                       -2.070e-01                       -1.483e-01  
mths_since_last_major_derog_cat  
                     -1.465e-01  


[[3]]

Call:
lm(formula = int_rate ~ ., data = train_data_fold)

Coefficients:
                    (Intercept)                        loan_amnt                       emp_length  
                      6.795e+00                        1.227e-04                        3.673e-03  
                 home_ownership              verification_status                          purpose  
                      1.796e-01                        8.496e-01                        3.794e-01  
                     addr_state                      delinq_2yrs                 earliest_cr_line  
                      2.056e-03                        4.228e-02                        2.071e-09  
                 inq_last_6mths                         open_acc                          pub_rec  
                      1.040e+00                        4.118e-02                        3.960e-01  
                      revol_bal                       revol_util                        total_acc  
                     -8.947e-06                        5.120e-02                       -2.648e-02  
            initial_list_status       collections_12_mths_ex_med                   acc_now_delinq  
                     -7.368e-01                        4.090e-01                        1.264e+00  
                   tot_coll_amt                      tot_cur_bal                      open_acc_6m  
                      3.001e-05                       -1.351e-06                        3.791e-03  
                     open_il_6m                      open_il_12m                      open_il_24m  
                     -1.259e-01                        7.328e-01                       -1.338e-01  
             mths_since_rcnt_il                     total_bal_il                          il_util  
                     -1.066e-02                        1.841e-06                       -6.795e-03  
                    open_rv_12m                      open_rv_24m                       max_bal_bc  
                      2.146e-01                       -7.199e-03                       -8.579e-05  
                       all_util                 total_rev_hi_lim                           inq_fi  
                      4.057e-03                       -1.006e-06                        5.499e-02  
                    total_cu_tl                     inq_last_12m                annual_inc_merged  
                     -5.518e-02                        6.357e-02                       -9.088e-06  
                     dti_merged            mths_since_delinq_cat       mths_since_last_record_cat  
                      6.126e-02                       -2.122e-01                       -2.423e-01  
mths_since_last_major_derog_cat  
                     -1.384e-01  


[[4]]

Call:
lm(formula = int_rate ~ ., data = train_data_fold)

Coefficients:
                    (Intercept)                        loan_amnt                       emp_length  
                      6.669e+00                        1.203e-04                        8.399e-03  
                 home_ownership              verification_status                          purpose  
                      1.705e-01                        8.574e-01                        3.508e-01  
                     addr_state                      delinq_2yrs                 earliest_cr_line  
                      9.598e-04                        5.734e-02                        2.017e-09  
                 inq_last_6mths                         open_acc                          pub_rec  
                      9.963e-01                        6.263e-02                        3.850e-01  
                      revol_bal                       revol_util                        total_acc  
                      1.191e-05                        4.117e-02                       -3.385e-02  
            initial_list_status       collections_12_mths_ex_med                   acc_now_delinq  
                     -6.315e-01                        2.786e-01                        1.662e+00  
                   tot_coll_amt                      tot_cur_bal                      open_acc_6m  
                      1.838e-05                       -9.500e-07                       -3.635e-02  
                     open_il_6m                      open_il_12m                      open_il_24m  
                     -1.334e-01                        4.343e-01                        1.271e-01  
             mths_since_rcnt_il                     total_bal_il                          il_util  
                     -8.521e-03                        4.237e-06                       -4.376e-03  
                    open_rv_12m                      open_rv_24m                       max_bal_bc  
                      7.466e-02                        1.385e-01                       -6.254e-05  
                       all_util                 total_rev_hi_lim                           inq_fi  
                     -7.971e-03                       -2.401e-05                        1.278e-01  
                    total_cu_tl                     inq_last_12m                annual_inc_merged  
                     -1.062e-01                        5.820e-02                       -4.855e-06  
                     dti_merged            mths_since_delinq_cat       mths_since_last_record_cat  
                      6.929e-02                       -1.944e-01                       -1.617e-01  
mths_since_last_major_derog_cat  
                     -1.483e-01  


[[5]]

Call:
lm(formula = int_rate ~ ., data = train_data_fold)

Coefficients:
                    (Intercept)                        loan_amnt                       emp_length  
                      6.625e+00                        1.279e-04                        1.136e-02  
                 home_ownership              verification_status                          purpose  
                      1.935e-01                        8.283e-01                        3.525e-01  
                     addr_state                      delinq_2yrs                 earliest_cr_line  
                      1.137e-03                       -6.451e-03                        2.030e-09  
                 inq_last_6mths                         open_acc                          pub_rec  
                      1.054e+00                        6.369e-02                        4.255e-01  
                      revol_bal                       revol_util                        total_acc  
                      6.297e-06                        4.456e-02                       -3.225e-02  
            initial_list_status       collections_12_mths_ex_med                   acc_now_delinq  
                     -5.496e-01                        5.413e-01                        1.546e+00  
                   tot_coll_amt                      tot_cur_bal                      open_acc_6m  
                      2.647e-05                       -9.294e-07                        3.598e-02  
                     open_il_6m                      open_il_12m                      open_il_24m  
                     -1.076e-01                        5.165e-01                        5.002e-02  
             mths_since_rcnt_il                     total_bal_il                          il_util  
                     -3.113e-03                        1.363e-06                       -1.340e-03  
                    open_rv_12m                      open_rv_24m                       max_bal_bc  
                      1.594e-01                       -2.279e-02                       -8.140e-05  
                       all_util                 total_rev_hi_lim                           inq_fi  
                     -8.735e-03                       -2.197e-05                        2.062e-02  
                    total_cu_tl                     inq_last_12m                annual_inc_merged  
                     -6.251e-02                        1.092e-01                       -7.380e-06  
                     dti_merged            mths_since_delinq_cat       mths_since_last_record_cat  
                      6.384e-02                       -2.054e-01                       -1.808e-01  
mths_since_last_major_derog_cat  
                     -1.441e-01  


[[6]]

Call:
lm(formula = int_rate ~ ., data = train_data_fold)

Coefficients:
                    (Intercept)                        loan_amnt                       emp_length  
                      6.226e+00                        1.216e-04                        3.531e-04  
                 home_ownership              verification_status                          purpose  
                      1.819e-01                        8.539e-01                        3.753e-01  
                     addr_state                      delinq_2yrs                 earliest_cr_line  
                      2.751e-04                        2.613e-02                        2.194e-09  
                 inq_last_6mths                         open_acc                          pub_rec  
                      1.050e+00                        4.567e-02                        5.423e-01  
                      revol_bal                       revol_util                        total_acc  
                     -8.489e-06                        5.094e-02                       -2.840e-02  
            initial_list_status       collections_12_mths_ex_med                   acc_now_delinq  
                     -7.601e-01                        4.038e-01                        1.302e+00  
                   tot_coll_amt                      tot_cur_bal                      open_acc_6m  
                      2.311e-05                       -1.091e-06                        1.343e-01  
                     open_il_6m                      open_il_12m                      open_il_24m  
                     -1.506e-01                        6.102e-01                        4.087e-02  
             mths_since_rcnt_il                     total_bal_il                          il_util  
                     -7.501e-03                        4.745e-06                       -3.830e-03  
                    open_rv_12m                      open_rv_24m                       max_bal_bc  
                      2.662e-01                       -1.898e-02                       -9.227e-05  
                       all_util                 total_rev_hi_lim                           inq_fi  
                     -4.138e-03                       -1.634e-06                       -5.819e-03  
                    total_cu_tl                     inq_last_12m                annual_inc_merged  
                     -4.751e-02                        5.149e-02                       -1.120e-05  
                     dti_merged            mths_since_delinq_cat       mths_since_last_record_cat  
                      5.727e-02                       -2.382e-01                       -9.641e-02  
mths_since_last_major_derog_cat  
                     -1.312e-01  


[[7]]

Call:
lm(formula = int_rate ~ ., data = train_data_fold)

Coefficients:
                    (Intercept)                        loan_amnt                       emp_length  
                      6.292e+00                        1.187e-04                        2.387e-03  
                 home_ownership              verification_status                          purpose  
                      1.676e-01                        8.765e-01                        3.491e-01  
                     addr_state                      delinq_2yrs                 earliest_cr_line  
                      1.294e-03                        1.753e-02                        2.087e-09  
                 inq_last_6mths                         open_acc                          pub_rec  
                      1.026e+00                        6.105e-02                        4.709e-01  
                      revol_bal                       revol_util                        total_acc  
                      3.357e-06                        4.449e-02                       -3.498e-02  
            initial_list_status       collections_12_mths_ex_med                   acc_now_delinq  
                     -6.449e-01                        2.629e-01                        1.268e+00  
                   tot_coll_amt                      tot_cur_bal                      open_acc_6m  
                      1.447e-05                       -1.594e-06                       -7.157e-02  
                     open_il_6m                      open_il_12m                      open_il_24m  
                     -4.692e-02                        4.124e-01                        8.638e-02  
             mths_since_rcnt_il                     total_bal_il                          il_util  
                     -7.308e-03                        9.496e-07                       -5.300e-03  
                    open_rv_12m                      open_rv_24m                       max_bal_bc  
                      7.600e-02                        1.171e-01                       -7.151e-05  
                       all_util                 total_rev_hi_lim                           inq_fi  
                     -8.874e-03                       -1.923e-05                        1.056e-02  
                    total_cu_tl                     inq_last_12m                annual_inc_merged  
                      1.132e-02                        3.502e-02                       -3.045e-06  
                     dti_merged            mths_since_delinq_cat       mths_since_last_record_cat  
                      7.089e-02                       -2.075e-01                       -1.125e-01  
mths_since_last_major_derog_cat  
                     -1.654e-01  


[[8]]

Call:
lm(formula = int_rate ~ ., data = train_data_fold)

Coefficients:
                    (Intercept)                        loan_amnt                       emp_length  
                      6.209e+00                        1.248e-04                        1.160e-02  
                 home_ownership              verification_status                          purpose  
                      1.773e-01                        8.651e-01                        3.504e-01  
                     addr_state                      delinq_2yrs                 earliest_cr_line  
                      5.853e-04                        3.050e-02                        2.052e-09  
                 inq_last_6mths                         open_acc                          pub_rec  
                      9.914e-01                        6.241e-02                        4.580e-01  
                      revol_bal                       revol_util                        total_acc  
                      5.356e-06                        4.453e-02                       -3.211e-02  
            initial_list_status       collections_12_mths_ex_med                   acc_now_delinq  
                     -6.198e-01                        3.945e-01                        1.584e+00  
                   tot_coll_amt                      tot_cur_bal                      open_acc_6m  
                      4.597e-05                       -1.178e-06                        5.436e-02  
                     open_il_6m                      open_il_12m                      open_il_24m  
                     -2.002e-01                        8.935e-01                       -1.549e-01  
             mths_since_rcnt_il                     total_bal_il                          il_util  
                     -1.179e-02                        2.674e-06                       -3.619e-03  
                    open_rv_12m                      open_rv_24m                       max_bal_bc  
                      1.913e-01                        5.839e-02                       -3.624e-05  
                       all_util                 total_rev_hi_lim                           inq_fi  
                     -5.312e-03                       -2.178e-05                        1.241e-01  
                    total_cu_tl                     inq_last_12m                annual_inc_merged  
                     -5.658e-02                        4.237e-02                       -6.659e-06  
                     dti_merged            mths_since_delinq_cat       mths_since_last_record_cat  
                      6.692e-02                       -1.977e-01                       -1.024e-01  
mths_since_last_major_derog_cat  
                     -1.458e-01  


[[9]]

Call:
lm(formula = int_rate ~ ., data = train_data_fold)

Coefficients:
                    (Intercept)                        loan_amnt                       emp_length  
                      6.183e+00                        1.192e-04                       -3.819e-03  
                 home_ownership              verification_status                          purpose  
                      1.472e-01                        8.480e-01                        3.663e-01  
                     addr_state                      delinq_2yrs                 earliest_cr_line  
                      3.031e-03                       -1.195e-02                        2.066e-09  
                 inq_last_6mths                         open_acc                          pub_rec  
                      9.837e-01                        5.603e-02                        4.285e-01  
                      revol_bal                       revol_util                        total_acc  
                      5.150e-06                        4.455e-02                       -2.954e-02  
            initial_list_status       collections_12_mths_ex_med                   acc_now_delinq  
                     -6.202e-01                        1.077e-01                        7.956e-01  
                   tot_coll_amt                      tot_cur_bal                      open_acc_6m  
                      3.526e-05                       -1.392e-06                        2.585e-02  
                     open_il_6m                      open_il_12m                      open_il_24m  
                     -1.490e-01                        6.185e-01                        2.844e-02  
             mths_since_rcnt_il                     total_bal_il                          il_util  
                     -4.387e-03                        4.846e-07                       -8.214e-04  
                    open_rv_12m                      open_rv_24m                       max_bal_bc  
                      4.166e-02                        1.129e-01                       -8.249e-05  
                       all_util                 total_rev_hi_lim                           inq_fi  
                     -5.746e-03                       -2.086e-05                       -2.847e-02  
                    total_cu_tl                     inq_last_12m                annual_inc_merged  
                     -8.818e-02                        7.265e-02                       -4.097e-06  
                     dti_merged            mths_since_delinq_cat       mths_since_last_record_cat  
                      6.711e-02                       -2.058e-01                       -1.159e-01  
mths_since_last_major_derog_cat  
                     -1.271e-01  


[[10]]

Call:
lm(formula = int_rate ~ ., data = train_data_fold)

Coefficients:
                    (Intercept)                        loan_amnt                       emp_length  
                      6.620e+00                        1.237e-04                        3.628e-03  
                 home_ownership              verification_status                          purpose  
                      1.518e-01                        8.846e-01                        3.535e-01  
                     addr_state                      delinq_2yrs                 earliest_cr_line  
                      2.738e-04                        5.111e-02                        2.013e-09  
                 inq_last_6mths                         open_acc                          pub_rec  
                      1.007e+00                        6.695e-02                        3.318e-01  
                      revol_bal                       revol_util                        total_acc  
                      5.070e-06                        4.422e-02                       -3.177e-02  
            initial_list_status       collections_12_mths_ex_med                   acc_now_delinq  
                     -6.139e-01                        1.075e-01                        1.207e+00  
                   tot_coll_amt                      tot_cur_bal                      open_acc_6m  
                      2.896e-05                       -1.315e-06                        5.319e-02  
                     open_il_6m                      open_il_12m                      open_il_24m  
                     -1.678e-01                        4.041e-01                        9.409e-02  
             mths_since_rcnt_il                     total_bal_il                          il_util  
                     -1.282e-02                        1.377e-06                        1.857e-04  
                    open_rv_12m                      open_rv_24m                       max_bal_bc  
                      3.216e-01                       -1.583e-02                       -9.745e-05  
                       all_util                 total_rev_hi_lim                           inq_fi  
                     -2.326e-03                       -2.255e-05                        4.121e-02  
                    total_cu_tl                     inq_last_12m                annual_inc_merged  
                     -1.113e-01                        7.710e-02                       -5.135e-06  
                     dti_merged            mths_since_delinq_cat       mths_since_last_record_cat  
                      6.467e-02                       -1.850e-01                       -2.054e-01  
mths_since_last_major_derog_cat  
                     -1.184e-01  
print(results)


#### Decision Trees ####

# Error in tree: "factor predictors must have at most 32 levels" is thrown.
# Basically, it becomes computationally expensive to create so many splits in your data, since you are selecting the best split out of all 2^32 (approx) possible splits.


# Fit a decision tree model on the training data
#tm <- tree(int_rate ~ ., data = sampled_train_data)

# Make predictions on the training and testing data
#tm.train_predictions <- predict(tm, newdata = sampled_train_data)
#tm.test_predictions <- predict(tm, newdata = sampled_test_data)

# Calculate Mean Squared Error (MSE) for training and testing
#tm.train_mse <- mean((tm.train_predictions - sampled_train_data$int_rate)^2)
#tm.test_mse <- mean((tm.test_predictions - sampled_test_data$int_rate)^2)

# Calculate Root Mean Squared Error (RMSE) for training and testing
#tm.train_rmse <- sqrt(tm.train_mse)
#tm.test_rmse <- sqrt(tm.test_mse)

# Calculate Mean Absolute Error (MAE) for training and testing
#tm.train_mae <- mean(abs(tm.train_predictions - sampled_train_data$int_rate))
#tm.test_mae <- mean(abs(tm.test_predictions - sampled_test_data$int_rate))

# Calculate R-squared (R²) for training and testing
#tm.train_r2 <- 1 - (sum((sampled_train_data$int_rate - tm.train_predictions)^2) / sum((sampled_train_data$int_rate - mean(sampled_train_data$int_rate))^2))
#tm.test_r2 <- 1 - (sum((sampled_test_data$int_rate - tm.test_predictions)^2) / sum((sampled_test_data$int_rate - mean(sampled_test_data$int_rate))^2))

# Display the metrics
#cat("Training MSE:", tm.train_mse, "\n")
#cat("Testing MSE:", tm.test_mse, "\n")
#cat("Training RMSE:", tm.train_rmse, "\n")
#cat("Testing RMSE:", tm.test_rmse, "\n")
#cat("Training MAE:", tm.train_mae, "\n")
#cat("Testing MAE:", tm.test_mae, "\n")
#cat("Training R-squared (R²):", tm.train_r2, "\n")
#cat("Testing R-squared (R²):", tm.test_r2, "\n")

#### Random Forest ####

# Train a Random Forest model
rf <- ranger(formula = int_rate ~ ., data = sampled_train_data, num.trees = 500, verbose=TRUE, importance = "impurity", oob.error = TRUE)
Growing trees.. Progress: 11%. Estimated remaining time: 4 minutes, 0 seconds.
Growing trees.. Progress: 24%. Estimated remaining time: 3 minutes, 17 seconds.
Growing trees.. Progress: 37%. Estimated remaining time: 2 minutes, 41 seconds.
Growing trees.. Progress: 50%. Estimated remaining time: 2 minutes, 7 seconds.
Growing trees.. Progress: 63%. Estimated remaining time: 1 minute, 33 seconds.
Growing trees.. Progress: 75%. Estimated remaining time: 1 minute, 2 seconds.
Growing trees.. Progress: 87%. Estimated remaining time: 33 seconds.
Growing trees.. Progress: 99%. Estimated remaining time: 1 seconds.
# Print the model summary
print("Random Forest Model Summary:")
[1] "Random Forest Model Summary:"
print(rf)
Ranger result

Call:
 ranger(formula = int_rate ~ ., data = sampled_train_data, num.trees = 500,      verbose = TRUE, importance = "impurity", oob.error = TRUE) 

Type:                             Regression 
Number of trees:                  500 
Sample size:                      638392 
Number of independent variables:  39 
Mtry:                             6 
Target node size:                 5 
Variable importance mode:         impurity 
Splitrule:                        variance 
OOB prediction error (MSE):       11.08217 
R squared (OOB):                  0.4229489 
# Make predictions on the training and testing data
rf.train_predictions <- predict(rf, data = sampled_train_data)
Predicting.. Progress: 73%. Estimated remaining time: 11 seconds.
rf.test_predictions <- predict(rf, data = sampled_test_data)

# Calculate Mean Squared Error (MSE) for training and testing
rf.train_mse <- mean((rf.train_predictions$predictions - sampled_train_data$int_rate)^2)
rf.test_mse <- mean((rf.test_predictions$predictions - sampled_test_data$int_rate)^2)

# Calculate Root Mean Squared Error (RMSE) for training and testing
rf.train_rmse <- sqrt(rf.train_mse)
rf.test_rmse <- sqrt(rf.test_mse)

# Calculate Mean Absolute Error (MAE) for training and testing
rf.train_mae <- mean(abs(rf.train_predictions$predictions - sampled_train_data$int_rate))
rf.test_mae <- mean(abs(rf.test_predictions$predictions - sampled_test_data$int_rate))

# Calculate R-squared (R²) for training and testing
rf.train_r2 <- 1 - (sum((sampled_train_data$int_rate - rf.train_predictions$predictions)^2) / sum((sampled_train_data$int_rate - mean(sampled_train_data$int_rate))^2))
rf.test_r2 <- 1 - (sum((sampled_test_data$int_rate - rf.test_predictions$predictions)^2) / sum((sampled_test_data$int_rate - mean(sampled_test_data$int_rate))^2))

# Display the metrics
cat("Training MSE:", rf.train_mse, "\n")
Training MSE: 2.572857 
cat("Testing MSE:", rf.test_mse, "\n")
Testing MSE: 11.01728 
cat("Training RMSE:", rf.train_rmse, "\n")
Training RMSE: 1.604013 
cat("Testing RMSE:", rf.test_rmse, "\n")
Testing RMSE: 3.319228 
cat("Training MAE:", rf.train_mae, "\n")
Training MAE: 1.260271 
cat("Testing MAE:", rf.test_mae, "\n")
Testing MAE: 2.6258 
cat("Training R-squared (R²):", rf.train_r2, "\n")
Training R-squared (R²): 0.8660306 
cat("Testing R-squared (R²):", rf.test_r2, "\n")
Testing R-squared (R²): 0.4260632 
#rf <- randomForest(int_rate~., data=train_data, ntree = 5, mtry = 3)
#bag.boston=randomForest(medv~.,data=Boston,subset=train, mtry=13,importance =TRUE)
#print(rf)

# Set the number of cores you want to use
#num_cores <- 6  # Adjust this number based on your system's capabilities

# Register parallel backend
#cl <- makeCluster(num_cores)
#registerDoParallel(cl)

# Assuming 'lc_data' is your dataset
#rf_model <- foreach(ntree = rep(100, num_cores), .packages = 'randomForest') %dopar% {
#    randomForest(int_rate ~ ., data = lc_data, ntree = ntree, mtry = sqrt(ncol(lc_data)))
#}

# After training, stop the cluster to release the cores:
#stopCluster(cl)

#### Boosting ####

# Define the target variable for training and testing
xgb.y_train <- sampled_train_data$int_rate
xgb.y_test <- sampled_test_data$int_rate  # Use sampled_test_data for testing

# Define the feature matrix for training and testing (exclude the target variable)
xgb.X_train <- sampled_train_data[, -which(names(sampled_train_data) == 'int_rate')]
xgb.X_test <- sampled_test_data[, -which(names(sampled_test_data) == 'int_rate')]  # Use sampled_test_data for testing

# Fit a gradient boosting regression model using xgboost
xgb <- xgboost(
  data = as.matrix(xgb.X_train),
  label = xgb.y_train,
  nrounds = 100,
  verbose = 0
)

# Make predictions on the training and testing data
xgb.train_predictions <- predict(xgb, newdata = as.matrix(xgb.X_train))
xgb.test_predictions <- predict(xgb, newdata = as.matrix(xgb.X_test))

# Calculate Mean Squared Error (MSE) for training and testing
xgb.train_mse <- mean((xgb.train_predictions - xgb.y_train)^2)
xgb.test_mse <- mean((xgb.test_predictions - xgb.y_test)^2)

# Calculate Root Mean Squared Error (RMSE) for training and testing
xgb.train_rmse <- sqrt(xgb.train_mse)
xgb.test_rmse <- sqrt(xgb.test_mse)

# Calculate Mean Absolute Error (MAE) for training and testing
xgb.train_mae <- mean(abs(xgb.train_predictions - xgb.y_train))
xgb.test_mae <- mean(abs(xgb.test_predictions - xgb.y_test))

# Calculate R-squared (R²) for training and testing
xgb.train_r2 <- 1 - (sum((xgb.y_train - xgb.train_predictions)^2) / sum((xgb.y_train - mean(xgb.y_train))^2))
xgb.test_r2 <- 1 - (sum((xgb.y_test - xgb.test_predictions)^2) / sum((xgb.y_test - mean(xgb.y_test))^2))

# Display the metrics
cat("Training MSE:", xgb.train_mse, "\n")
Training MSE: 9.918589 
cat("Testing MSE:", xgb.test_mse, "\n")
Testing MSE: 10.29675 
cat("Training RMSE:", xgb.train_rmse, "\n")
Training RMSE: 3.149379 
cat("Testing RMSE:", xgb.test_rmse, "\n")
Testing RMSE: 3.208854 
cat("Training MAE:", xgb.train_mae, "\n")
Training MAE: 2.475425 
cat("Testing MAE:", xgb.test_mae, "\n")
Testing MAE: 2.522647 
cat("Training R-squared (R²):", xgb.train_r2, "\n")
Training R-squared (R²): 0.4835362 
cat("Testing R-squared (R²):", xgb.test_r2, "\n")
Testing R-squared (R²): 0.4635987 

Following, a scatter plot of actual vs predicted training values for each model is plot. This plot helps us visualize how well each model’s predictions align with the actual data points.

# Create a scatter plot function
create_scatter_plot <- function(actual_values, predicted_values, model_name) {
  model_comparison_data <- data.frame(
    Actual = actual_values,
    Predicted = predicted_values
  )
  
  scatter_plot <- ggplot(model_comparison_data, aes(x = Actual, y = Predicted)) +
    geom_point() +
    geom_abline(intercept = 0, slope = 1, linetype = "dashed", color = "red") +  # Add a diagonal reference line
    labs(x = "Actual Training Values", y = "Predicted Training Values", title = model_name) +
    theme_minimal() +
    ylim(-50, 50)
  
  return(scatter_plot)
}

# Create scatter plots for each model
lm_scatter_plot <- create_scatter_plot(
  actual_values = sampled_train_data$int_rate,
  predicted_values = lm.train_predictions,
  model_name = "Linear Regression"
)

rf_scatter_plot <- create_scatter_plot(
  actual_values = sampled_train_data$int_rate,
  predicted_values = rf.train_predictions$predictions,
  model_name = "Random Forest"
)

xgb_scatter_plot <- create_scatter_plot(
  actual_values = xgb.y_train,
  predicted_values = xgb.train_predictions,
  model_name = "XGBoost"
)

# Display the scatter plots separately
print(lm_scatter_plot)

print(rf_scatter_plot)

print(xgb_scatter_plot)

Following, a scatter plot of actual vs predicted testing values for each model is plot. This plot helps us visualize how well each model’s predictions align with the actual data points.

# Create a scatter plot function
create_scatter_plot <- function(actual_values, predicted_values, model_name) {
  model_comparison_data <- data.frame(
    Actual = actual_values,
    Predicted = predicted_values
  )
  
  scatter_plot <- ggplot(model_comparison_data, aes(x = Actual, y = Predicted)) +
    geom_point() +
    geom_abline(intercept = 0, slope = 1, linetype = "dashed", color = "red") +  # Add a diagonal reference line
    labs(x = "Actual Testing Values", y = "Predicted Testing Values", title = model_name) +
    theme_minimal() +
    ylim(-50, 50)
  
  return(scatter_plot)
}

# Create scatter plots for each model
lm_scatter_plot <- create_scatter_plot(
  actual_values = sampled_test_data$int_rate,
  predicted_values = lm.test_predictions,
  model_name = "Linear Regression"
)

rf_scatter_plot <- create_scatter_plot(
  actual_values = sampled_test_data$int_rate,
  predicted_values = rf.test_predictions$predictions,
  model_name = "Random Forest"
)

xgb_scatter_plot <- create_scatter_plot(
  actual_values = xgb.y_test,
  predicted_values = xgb.test_predictions,
  model_name = "XGBoost"
)

# Display the scatter plots separately
print(lm_scatter_plot)

print(rf_scatter_plot)

print(xgb_scatter_plot)

Residual plots can help identify patterns in prediction errors and assess whether the assumptions of linear regression (if applicable) are met.

# Create a residual plot function
create_residual_plot <- function(actual_values, predicted_values, model_name) {
  residuals <- actual_values - predicted_values
  residual_data <- data.frame(
    Predicted = predicted_values,
    Residuals = residuals
  )
  
  residual_plot <- ggplot(residual_data, aes(x = Predicted, y = Residuals)) +
    geom_point() +
    geom_hline(yintercept = 0, linetype = "dashed", color = "red") +  # Red horizontal reference line
    labs(x = "Predicted Values", y = "Residuals", title = paste("Residual Plot -", model_name)) +
    theme_minimal() +
    ylim(-30, 30) +
    xlim(0, 40)
  
  return(residual_plot)
}

# Create residual plots for each model
lm_residual_plot <- create_residual_plot(
  actual_values = sampled_train_data$int_rate,
  predicted_values = lm.train_predictions,
  model_name = "Linear Regression"
)

rf_residual_plot <- create_residual_plot(
  actual_values = sampled_train_data$int_rate,
  predicted_values = rf.train_predictions$predictions,
  model_name = "Random Forest"
)

xgb_residual_plot <- create_residual_plot(
  actual_values = xgb.y_train,
  predicted_values = xgb.train_predictions,
  model_name = "XGBoost"
)

# Display the residual plots separately
print(lm_residual_plot)

print(rf_residual_plot)

print(xgb_residual_plot)

From the plots above we can clearly see that:

This visualization can help you compare the distribution of prediction errors across models.

# Create a density plot function for residuals
create_residual_density_plot <- function(actual_values, predicted_values, model_name) {
  residuals <- actual_values - predicted_values
  residual_data <- data.frame(Residuals = residuals)
  
  density_plot <- ggplot(residual_data, aes(x = Residuals)) +
    geom_density(fill = "skyblue", color = "black", alpha = 0.7) +
    labs(x = "Residuals", y = "Density", title = paste("Residual Density Plot -", model_name)) +
    theme_minimal()
  
  return(density_plot)
}

# Create density plots for residuals for each model
lm_residual_density_plot <- create_residual_density_plot(
  actual_values = sampled_train_data$int_rate,
  predicted_values = lm.train_predictions,
  model_name = "Linear Regression"
)

rf_residual_density_plot <- create_residual_density_plot(
  actual_values = sampled_train_data$int_rate,
  predicted_values = rf.train_predictions$predictions,
  model_name = "Random Forest"
)

xgb_residual_density_plot <- create_residual_density_plot(
  actual_values = xgb.y_train,
  predicted_values = xgb.train_predictions,
  model_name = "XGBoost"
)

# Display the density plots separately
print(lm_residual_density_plot)

print(rf_residual_density_plot)

print(xgb_residual_density_plot)

This visualization can help you compare the distribution of prediction errors across models through histograms.

# Create a histogram plot function for residuals with a red density curve
create_residual_histogram_plot <- function(actual_values, predicted_values, model_name) {
  residuals <- actual_values - predicted_values
  residual_data <- data.frame(Residuals = residuals)
  
  histogram_plot <- ggplot(residual_data, aes(x = Residuals)) +
    geom_histogram(aes(y = after_stat(density)), bins = 30, fill = "skyblue", color = "black", alpha = 0.7) +  # Use density on the y-axis for the histogram
    geom_density(color = "red", linewidth = 1.5) +  # Add the density plot in red
    labs(x = "Residuals", y = "Density", title = paste("Residual Histogram Plot with Density Curve -", model_name)) +
    theme_minimal() +
    xlim(-20,20) + 
    ylim(0, 0.3)
  
  return(histogram_plot)
}

# Create histogram plots for residuals for each model
lm_residual_histogram_plot <- create_residual_histogram_plot(
  actual_values = sampled_train_data$int_rate,
  predicted_values = lm.train_predictions,
  model_name = "Linear Regression"
)

rf_residual_histogram_plot <- create_residual_histogram_plot(
  actual_values = sampled_train_data$int_rate,
  predicted_values = rf.train_predictions$predictions,
  model_name = "Random Forest"
)

xgb_residual_histogram_plot <- create_residual_histogram_plot(
  actual_values = xgb.y_train,
  predicted_values = xgb.train_predictions,
  model_name = "XGBoost"
)

# Display the histogram plots separately
print(lm_residual_histogram_plot)

print(rf_residual_histogram_plot)

print(xgb_residual_histogram_plot)

For each model a bar chart that displays the R-squared (coefficient of determination) values is created. R-squared measures the proportion of variance in the target variable explained by the model. Higher R-squared values indicate better model fit.

# Create a data frame with R-squared values for each model
model_names <- c("Linear Regression", "Random Forest", "XGBoost")
r_squared_values <- c(
  lm.train_r2,
  rf.train_r2,
  xgb.train_r2
)

r_squared_data <- data.frame(Model = factor(model_names),
                              R_squared = r_squared_values)

# Create the R-squared comparison bar chart
r_squared_bar_chart <- ggplot(r_squared_data, aes(x = Model, y = R_squared, fill = Model)) +
  geom_bar(stat = "identity") +
  labs(x = "Model", y = "R-squared (R²)", title = "R-squared Comparison") +
  theme_minimal() +
  theme(axis.text.x = element_text(angle = 45, hjust = 1))

# Display the R-squared comparison bar chart
print(r_squared_bar_chart)

A bar chart that compares the MAE or RMSE values, is generated for each model. These metrics quantify the average prediction errors of each model, and lower values are preferred.

# Create a data frame with MAE and RMSE values for each model
model_names <- c("Linear Regression", "Random Forest", "XGBoost","Linear Regression", "Random Forest", "XGBoost")
error_values_train <- c(
  lm.train_mae,
  rf.train_mae,
  xgb.train_mae,
  lm.train_rmse,
  rf.train_rmse,
  xgb.train_rmse
)
error_values_test <- c(
  lm.test_mae,
  rf.test_mae,
  xgb.test_mae,
  lm.test_rmse,
  rf.test_rmse,
  xgb.test_rmse
)
error_type <- c(
  "MAE", "MAE", "MAE","RMSE","RMSE","RMSE"
)
model_errors_train <- data.frame(Model = factor(model_names, levels = c("Linear Regression", "Random Forest", "XGBoost")),
                Error = error_values_train, Type = error_type)
model_errors_test <- data.frame(Model = factor(model_names, levels = c("Linear Regression", "Random Forest", "XGBoost")),
                Error = error_values_test, Type = error_type)
# Create the MAE or RMSE comparison bar chart
error_bar_chart_train <- ggplot(model_errors_train, aes(x = Model, y = Error, fill = Type)) +
  geom_bar(stat = "identity", position = "dodge") +
  labs(x = "Model", y = "Error Value", title = "Training MAE and RMSE Comparison") +
  theme_minimal() +
  theme(axis.text.x = element_text(angle = 45, hjust = 1)) + 
  ylim(0, 4)

error_bar_chart_test <- ggplot(model_errors_test, aes(x = Model, y = Error, fill = Type)) +
  geom_bar(stat = "identity", position = "dodge") +
  labs(x = "Model", y = "Error Value", title = "Testing MAE and RMSE Comparison") +
  theme_minimal() +
  theme(axis.text.x = element_text(angle = 45, hjust = 1)) + 
  ylim(0, 4)

# Display the MAE and RMSE comparison bar chart
print(error_bar_chart_train)

print(error_bar_chart_test)

#### Random Forest Feature Importance Plot ####
v1 <- vip(rf, title = "Ranger", num_features = 20) 
plot(v1)

Learning curve using RMSE and R^2:

# TODO: change the x-axes
# Create a data frame with RMSE and R-squared values for each model and sample size
model_names <- c("Linear Regression", "Random Forest", "XGBoost")
sample_sizes <- seq(10, nrow(sampled_train_data), by = 10)  # Adjust the sample sizes as needed

# Create data frames with RMSE and R-squared values for each model
rmse_data <- data.frame(
  Model = rep(model_names, each = length(sample_sizes)),
  Sample_Size = rep(sample_sizes, times = length(model_names)),
  RMSE = c(
    lm.train_rmse, rf.train_rmse, xgb.train_rmse
  )
)

r_squared_data <- data.frame(
  Model = rep(model_names, each = length(sample_sizes)),
  Sample_Size = rep(sample_sizes, times = length(model_names)),
  R_squared = c(
    lm.train_r2, rf.train_r2, xgb.train_r2
  )
)

# Create RMSE learning curve
rmse_curve <- ggplot(rmse_data, aes(x = Sample_Size, y = RMSE, color = Model)) +
  geom_line() +
  labs(x = "Sample Size", y = "RMSE", title = "RMSE Learning Curve") +
  theme_minimal()

# Create R-squared learning curve
r_squared_curve <- ggplot(r_squared_data, aes(x = Sample_Size, y = R_squared, color = Model)) +
  geom_line() +
  labs(x = "Sample Size", y = "R-squared", title = "R-squared Learning Curve") +
  theme_minimal()

# Display the RMSE and R-squared learning curves
print(rmse_curve)

print(r_squared_curve)

Add a new chunk by clicking the Insert Chunk button on the toolbar or by pressing Ctrl+Alt+I.

When you save the notebook, an HTML file containing the code and output will be saved alongside it (click the Preview button or press Ctrl+Shift+K to preview the HTML file).

The preview shows you a rendered HTML copy of the contents of the editor. Consequently, unlike Knit, Preview does not run any R code chunks. Instead, the output of the chunk when it was last run in the editor is displayed.

---
title: "R Notebook"
output: html_notebook
---

# Data Pre-processing

Load needed libraries

```{r}
library(fastDummies)
library(readr)
library(ggplot2)
library(dplyr)
library(caret)
library(glmnet)
library(boot)
library(tree)
library(ranger)
library(xgboost)
library(gbm)
library(vip)
library(ISLR)
```

Set the seed for reproducibility

```{r}
set.seed(1)
```

Load the dataset

```{r}
original_lc_data <- read.csv("LCdata.csv",sep = ";")
lc_data <- original_lc_data
```

remove attributes not available for prediction

```{r}
lc_data <- subset(lc_data, select = -c(collection_recovery_fee, installment, issue_d,
                                       last_pymnt_amnt, last_pymnt_d, loan_status,
                                       next_pymnt_d, out_prncp, out_prncp_inv,
                                       pymnt_plan, recoveries,
                                       term, total_pymnt,
                                       total_pymnt_inv,total_rec_int, total_rec_late_fee,                                                  total_rec_prncp))

```

```{r}
summary(lc_data)
```

First we delete the columns which aren't useful for our prediction

```{r}
lc_data$id <- NULL
lc_data$member_id <- NULL
lc_data$zip_code <- NULL
lc_data$url <- NULL
```
Looks like **policy_code** contains just value equal to 1, it can be removed
```{r}
lc_data$policy_code <- NULL
```
Remove additional columns which are related to the historical data
```{r}
lc_data$last_credit_pull_d <- NULL
```

Then we delete the columns which can't be converted to categorical and require NLP

```{r}
lc_data$title <- NULL
lc_data$desc <- NULL
lc_data$emp_title <- NULL

```

let's examine the **loan_amnt** column

```{r}
sum(is.na(lc_data$loan_amnt))
cor(lc_data$loan_amnt, lc_data$int_rate)
hist(lc_data$loan_amnt, breaks = 20, main = "loan_amnt distribution", xlab = "loan_amnt", col = "lightblue", border = "black")
ggplot(data = lc_data, mapping = aes(x=int_rate,y=loan_amnt)) + geom_boxplot()
```

standardize **loan_amnt**

```{r}
#lc_data$loan_amnt <- scale(lc_data$loan_amnt)
```

let's examine the **funded_amnt** column

```{r}
sum(is.na(lc_data$funded_amnt))
cor(lc_data$funded_amnt, lc_data$int_rate)
hist(lc_data$funded_amnt, breaks = 20, main = "funded_amnt distribution", xlab = "funded_amnt", col = "lightblue", border = "black")
```

as we can see, **funded_amnt** is almost the same as the **loan_amnt** column, consequently, we remove it.

```{r}
lc_data$funded_amnt <- NULL 
```

let's examine the **funded_amnt_inv** column

```{r}
sum(is.na(lc_data$funded_amnt_inv))
cor(lc_data$funded_amnt_inv, lc_data$int_rate)
hist(lc_data$funded_amnt_inv, breaks = 20, main = "funded_amnt_inv distribution", xlab = "funded_amnt_inv", col = "lightblue", border = "black")
```

remove **funded_amnt_inv** for the same reason as above

```{r}
lc_data$funded_amnt_inv <- NULL
```

let's see the **int_rate** distribution.
```{r}
hist(lc_data$int_rate, breaks = 20, main = "int_rate distribution", xlab = "int_rate", col = "lightblue", border = "black")
```
Standardize int rate:
```{r}
#lc_data$int_rate <- scale(lc_data$int_rate)
```
we delete the **emp_title** column as there are several entries for the same job title and because there are too many different values for one-hot encoding. In addition, some titles are unclear (NLP required)
```{r}
n_distinct(lc_data$emp_title)
```
As we can observe, there are 40363 NAs. We can assume 40363 do not work.
```{r}
barplot(table(lc_data$emp_length),
        xlab = "emp_length years", 
        ylab = "Frequency", 
        col = "skyblue", 
        border = "black",
        cex.names = 0.6)  # The size of the main title
```

Since **emp_length** seems to be categorical, we transform it to as a factor and then as numeric.
The conversion to numeric is needed for supporting the XGBoost 
```{r}
lc_data$emp_length <- as.factor(lc_data$emp_length)
ggplot(data = lc_data, mapping = aes(x=int_rate,y=emp_length)) + geom_boxplot()
lc_data$emp_length <- as.numeric(lc_data$emp_length)
```


Cleaning of **home_ownership**:

During the data cleaning phase, our analysis revealed that the variable "home_ownership" does not show a distinct correlation with interest rates. Specifically, among the categories, "ANY" and "OTHER" contain 2 and 154 cases, respectively, while the "NONE" category comprises 39 cases. Although the "NONE" category appears to demonstrate a higher interest rate compared to others, the limited sample size of 39 cases raises doubts about the reliability of this observation. Notably, the "NONE" category might pertain to individuals experiencing homelessness, prompting ethical concerns about loan provision to this demographic.

```{r}
table(lc_data$home_ownership)
ggplot(data = lc_data, mapping = aes(x=int_rate,y=home_ownership)) + geom_boxplot()
```
Then, we retain mortgage, own and rent:
```{r}
lc_data <- lc_data %>% filter(home_ownership %in% c("MORTGAGE","OWN","RENT"))
lc_data$home_ownership <- as.numeric(as.factor(lc_data$home_ownership))
```

# application joint handling
```{r}

# merging annual income
lc_data <- lc_data %>% mutate(
    annual_inc_merged = ifelse(is.na(annual_inc_joint)== TRUE, annual_inc,annual_inc_joint)) 

lc_data <- lc_data %>% select(-annual_inc,-annual_inc_joint)


# merging debt to income ratio
lc_data <- lc_data %>% mutate(
    dti_merged = ifelse(is.na(dti_joint)== TRUE, dti,dti_joint)) 

lc_data <- lc_data %>% select(-dti,-dti_joint)

```

Upon reviewing the summary again, it becomes apparent that there are merely 460 joint applications, constituting a small subset within the extensive dataset of around 800k rows. Through consolidating the debt-to-income ratios (dti's), we can pinpoint the data pertinent to our research objectives. Hence, it is advisable to eliminate the columns verification_status_joint and application_type to prevent introducing unwarranted variability into our analysis.

```{r}
table(lc_data$verification_status)
table(lc_data$verification_status_joint)
```

```{r}
lc_data$verification_status <- as.numeric(as.factor(lc_data$verification_status))
lc_data <- lc_data %>% select(-verification_status_joint, -application_type)
```


Let's checl if other is NA or a real value for purpose. It's a real one, so we don't have to handle it.
```{r}
lc_data$purpose <- as.factor(lc_data$purpose)
ggplot(data = lc_data, mapping = aes(x=int_rate,y=purpose)) + geom_boxplot()
lc_data$purpose <- as.numeric(lc_data$purpose)
```
Let's have a glance to the state address:
```{r}
table(lc_data$addr_state)
lc_data$addr_state <- as.factor(lc_data$addr_state)
ggplot(data = lc_data, mapping = aes(x=int_rate,y=addr_state)) + geom_boxplot()
lc_data$addr_state <- as.numeric(lc_data$addr_state)
```
Regarding delinquency in the last 2 years, there are few NAs then remove them:
```{r}
lc_data <- lc_data %>% 
    filter(!(is.na(delinq_2yrs)))
```


```{r}
lc_data <- lc_data %>%
  mutate(mths_since_delinq_cat = ifelse(
    is.na(mths_since_last_delinq) == TRUE,
    "NONE",
    ifelse(
      mths_since_last_delinq <= 12,
      "Less_1_Y",
      ifelse(
        mths_since_last_delinq <= 24,
        "Less_2_Y",
        ifelse(
          mths_since_last_delinq <= 36,
          "Less_3_Y",
          ifelse(mths_since_last_delinq <= 48, "Less_4_Y", "More_4_Y")
        )
      )
    )
  )) %>% select(-mths_since_last_delinq)
          
lc_data$mths_since_delinq_cat <- as.factor(lc_data$mths_since_delinq_cat)
ggplot(data = lc_data, mapping = aes(x=int_rate,y=mths_since_delinq_cat))+geom_boxplot()
lc_data$mths_since_delinq_cat <- as.numeric(lc_data$mths_since_delinq_cat)
```

```{r}
lc_data <- lc_data %>%
  mutate(mths_since_last_record_cat = ifelse(
    is.na(mths_since_last_record) == TRUE,
    "NONE",
    ifelse(
      mths_since_last_record <= 12,
      "Less_1_Y",
      ifelse(
        mths_since_last_record <= 24,
        "Less_2_Y",
        ifelse(
          mths_since_last_record <= 36,
          "Less_3_Y",
          ifelse(mths_since_last_record <= 48, "Less_4_Y", "More_4_Y")
        )
      )
    )
  )) %>% select(-mths_since_last_record)

lc_data$mths_since_last_record_cat <- as.factor(lc_data$mths_since_last_record_cat)
ggplot(data = lc_data, mapping = aes(x=int_rate,y=mths_since_last_record_cat))+geom_boxplot()
lc_data$mths_since_last_record_cat <- as.numeric(lc_data$mths_since_last_record_cat)
```

```{r}
lc_data <-lc_data %>% 
  mutate(mths_since_last_major_derog_cat =  ifelse(
    is.na(mths_since_last_major_derog) == TRUE,
    "NONE",
    ifelse(
      mths_since_last_major_derog <= 12,
      "Less_1_Y",
      ifelse(
        mths_since_last_major_derog <= 24,
        "Less_2_Y",
        ifelse(
          mths_since_last_major_derog <= 36,
          "Less_3_Y",
          ifelse(mths_since_last_major_derog <= 48, "Less_4_Y", "More_4_Y")
        )
      )
    )
  )) %>% select(-mths_since_last_major_derog)

lc_data$mths_since_last_major_derog_cat <- as.factor(lc_data$mths_since_last_major_derog_cat)
ggplot(data = lc_data, mapping = aes(x=int_rate,y=mths_since_last_major_derog_cat))+geom_boxplot()
lc_data$mths_since_last_major_derog_cat <- as.numeric(lc_data$mths_since_last_major_derog_cat)

```

```{r}
lc_data$initial_list_status <- as.factor(lc_data$initial_list_status)
ggplot(data = lc_data, mapping = aes(x=int_rate,y=initial_list_status))+geom_boxplot()
lc_data$initial_list_status <- as.numeric(lc_data$initial_list_status)
```

Let's check which columns still have null values
```{r}
colSums(is.na(lc_data))
```
The columns **revol_bal** and **revol_util** contain only few NA values, those values can't be replaced with 0, then we filter the values which are not NA
```{r}
lc_data <- lc_data %>% 
    filter(!(is.na(revol_bal))) %>% 
        filter(!(is.na(revol_util)))
```


Let's check which columns still have null values
```{r}
names(which(colSums(is.na(lc_data)) > 0))
```

Replace null values with 0 where is possible
```{r}
lc_data <-
  lc_data %>%
  mutate(open_acc_6m = ifelse(is.na(open_acc_6m) == TRUE, 0, open_acc_6m)) %>%
  mutate(tot_cur_bal = ifelse(is.na(tot_cur_bal) == TRUE, 0, tot_cur_bal)) %>%
  mutate(open_il_6m = ifelse(is.na(open_il_6m) == TRUE, 0, open_il_6m)) %>%
  mutate(open_il_12m = ifelse(is.na(open_il_12m) == TRUE, 0, open_il_12m)) %>%
  mutate(open_il_24m = ifelse(is.na(open_il_24m) == TRUE, 0, open_il_24m)) %>%
  mutate(mths_since_rcnt_il = ifelse(is.na(mths_since_rcnt_il) == TRUE, 0, mths_since_rcnt_il)) %>%
  mutate(total_bal_il = ifelse(is.na(total_bal_il) == TRUE, 0, total_bal_il)) %>%
  mutate(il_util = ifelse(is.na(il_util) == TRUE, 0, il_util)) %>%
  mutate(open_rv_12m = ifelse(is.na(open_rv_12m) == TRUE, 0, open_rv_12m)) %>%
  mutate(total_rev_hi_lim = ifelse(is.na(total_rev_hi_lim) == TRUE, 0, total_rev_hi_lim)) %>%
  mutate(max_bal_bc = ifelse(is.na(max_bal_bc) == TRUE, 0, max_bal_bc)) %>%
  mutate(all_util = ifelse(is.na(all_util) == TRUE, 0, all_util)) %>%
  mutate(inq_fi = ifelse(is.na(inq_fi) == TRUE, 0, inq_fi)) %>%
  mutate(total_cu_tl = ifelse(is.na(total_cu_tl) == TRUE, 0, total_cu_tl)) %>%
  mutate(inq_last_12m = ifelse(is.na(inq_last_12m) == TRUE, 0, inq_last_12m)) %>%
  mutate(open_rv_24m = ifelse(is.na(open_rv_24m) == TRUE, 0, open_rv_24m)) %>%
  mutate(tot_coll_amt = ifelse(is.na(tot_coll_amt)== TRUE,0, tot_coll_amt)) %>%
  mutate(collections_12_mths_ex_med = ifelse(is.na(collections_12_mths_ex_med)== TRUE,0, collections_12_mths_ex_med))
```

**earliest_cr_line** contains the month the borrower's earliest reported credit line was opened.
Even if this date consists only on month and year, still there are too many unique values.
We could transform the dates in to a numerical value, by converting them from date into Unix Time.
This unit measures time by the number of seconds that have elapsed since 00:00:00 UTC on 1 January 1970.
Since this column doesn't contain the day number, we take as a reference the first day of the month.

```{r}
lc_data <- lc_data %>% 
    filter(!(is.na(earliest_cr_line)))

# function to replace dates with unix time
to_unix_time <- function(date) {
  tmp <- paste("01", date, sep="-")
  return (as.numeric(as.POSIXct(tmp, format="%d-%b-%Y", tz="UTC")))
}

# map dates to unix time
lc_data$earliest_cr_line <- apply(lc_data, 1, function(row) to_unix_time(row["earliest_cr_line"]))

# standardize them
#lc_data$earliest_cr_line <- scale(lc_data$earliest_cr_line)
```

```{r}
summary(lc_data)
```


```{r}
#round(cor(lc_data),2)
```

```{r}

# TODO: (parte vecchia), split 80/20 e linear regression...
# Create indices for splitting (80% train, 20% test)
train_indices <- createDataPartition(lc_data$int_rate, p = 0.8, list = FALSE)

# Create training and testing datasets
train_data <- lc_data[train_indices, ]
test_data <- lc_data[-train_indices, ]

#### Linear Regression ####
#lm.fit <- lm(int_rate ~ ., data = train_data)

# TODO: check collinearity and multicollinearity
#vif(lm.fit) # there is multicollinearity
#cor(lc_data) 

# Make predictions on training and testing data
#train_predictions <- predict(lm.fit, newdata = train_data)
#test_predictions <- predict(lm.fit, newdata = test_data)

# Evaluate model performance on training data
#train_rmse <- sqrt(mean((train_predictions - train_data$int_rate)^2))
#train_r_squared <- summary(lm.fit)$r.squared

# Evaluate model performance on testing data
#test_rmse <- sqrt(mean((test_predictions - test_data$int_rate)^2))
#test_r_squared <- summary(lm.fit, test_data)$r.squared

# Print evaluation metrics
#cat("Training RMSE:", train_rmse, "\n")
#cat("Training R-squared:", train_r_squared, "\n")
#rmse <- sqrt(mean(lm.fit$residuals^2))
#print(rmse)
```

```{r}
# 1% of the total rows
sample_train_size <- floor(0.01 * nrow(train_data))
sample_test_size <- floor(0.01 * nrow(test_data))

# Randomly select 1% of the rows
sampled_train_data <- train_data[sample(nrow(train_data), size = sample_train_size, replace = FALSE), ]
sampled_test_data <- test_data[sample(nrow(test_data), size = sample_test_size, replace = FALSE), ]

sampled_train_data <- train_data
sampled_test_data <- test_data

#### Linear Regression ####

lm.fit <- lm(int_rate ~ ., data = sampled_train_data)

# Make predictions on the training and testing data
lm.train_predictions <- predict(lm.fit, newdata = sampled_train_data)
lm.test_predictions <- predict(lm.fit, newdata = sampled_test_data)

# Calculate Mean Squared Error (MSE) for training and testing
lm.train_mse <- mean((lm.train_predictions - sampled_train_data$int_rate)^2)
lm.test_mse <- mean((lm.test_predictions - sampled_test_data$int_rate)^2)

# Calculate Root Mean Squared Error (RMSE) for training and testing
lm.train_rmse <- sqrt(lm.train_mse)
lm.test_rmse <- sqrt(lm.test_mse)

# Calculate Mean Absolute Error (MAE) for training and testing
lm.train_mae <- mean(abs(lm.train_predictions - sampled_train_data$int_rate))
lm.test_mae <- mean(abs(lm.test_predictions - sampled_test_data$int_rate))

# Calculate R-squared (R²) for training and testing
lm.train_r2 <- 1 - (sum((sampled_train_data$int_rate - lm.train_predictions)^2) / sum((sampled_train_data$int_rate - mean(sampled_train_data$int_rate))^2))
lm.test_r2 <- 1 - (sum((sampled_test_data$int_rate - lm.test_predictions)^2) / sum((sampled_test_data$int_rate - mean(sampled_test_data$int_rate))^2))

# Display the metrics
cat("Training MSE:", lm.train_mse, "\n")
cat("Testing MSE:", lm.test_mse, "\n")
cat("Training RMSE:", lm.train_rmse, "\n")
cat("Testing RMSE:", lm.test_rmse, "\n")
cat("Training MAE:", lm.train_mae, "\n")
cat("Testing MAE:", lm.test_mae, "\n")
cat("Training R-squared (R²):", lm.train_r2, "\n")
cat("Testing R-squared (R²):", lm.test_r2, "\n")

#### Linear Regresion applying Cross Validation with k=2 to k=10  ####


# Assuming 'sampled_train_data' is your training data set

# Initialize lists to store models and their results
models <- list()
results <- data.frame()

# Define the number of folds for cross-validation
num_folds <- 10
folds <- createFolds(sampled_train_data$int_rate, k = num_folds, list = TRUE)

# Perform k-fold cross-validation
for(i in seq_along(folds)) {
  # Split the data into training and testing for the current fold
  train_indices <- folds[[i]]
  test_indices <- setdiff(seq_len(nrow(sampled_train_data)), train_indices)
  
  train_data_fold <- sampled_train_data[train_indices, ]
  test_data_fold <- sampled_train_data[test_indices, ]
  
  # Fit the model on the training fold
  lm_model <- lm(int_rate ~ ., data = train_data_fold)
  models[[i]] <- lm_model  # Store the model
  
  # Make predictions on the training and testing fold
  train_predictions <- predict(lm_model, newdata = train_data_fold)
  test_predictions <- predict(lm_model, newdata = test_data_fold)
  
  # Calculate metrics for training fold
  train_mse <- mean((train_predictions - train_data_fold$int_rate)^2)
  train_rmse <- sqrt(train_mse)
  train_mae <- mean(abs(train_predictions - train_data_fold$int_rate))
  train_r2 <- summary(lm_model)$r.squared
  
  # Calculate metrics for testing fold
  test_mse <- mean((test_predictions - test_data_fold$int_rate)^2)
  test_rmse <- sqrt(test_mse)
  test_mae <- mean(abs(test_predictions - test_data_fold$int_rate))
  test_r2 <- 1 - (sum((test_data_fold$int_rate - test_predictions)^2) / sum((test_data_fold$int_rate - mean(test_data_fold$int_rate))^2))
  
  # Store metrics in the results dataframe
  results <- rbind(results, data.frame(
    Fold = i,
    Train_MSE = train_mse, Test_MSE = test_mse,
    Train_RMSE = train_rmse, Test_RMSE = test_rmse,
    Train_MAE = train_mae, Test_MAE = test_mae,
    Train_R2 = train_r2, Test_R2 = test_r2
  ))
}

# Display the models and their metrics
print(models)
print(results)


#### Decision Trees ####

# Error in tree: "factor predictors must have at most 32 levels" is thrown.
# Basically, it becomes computationally expensive to create so many splits in your data, since you are selecting the best split out of all 2^32 (approx) possible splits.


# Fit a decision tree model on the training data
#tm <- tree(int_rate ~ ., data = sampled_train_data)

# Make predictions on the training and testing data
#tm.train_predictions <- predict(tm, newdata = sampled_train_data)
#tm.test_predictions <- predict(tm, newdata = sampled_test_data)

# Calculate Mean Squared Error (MSE) for training and testing
#tm.train_mse <- mean((tm.train_predictions - sampled_train_data$int_rate)^2)
#tm.test_mse <- mean((tm.test_predictions - sampled_test_data$int_rate)^2)

# Calculate Root Mean Squared Error (RMSE) for training and testing
#tm.train_rmse <- sqrt(tm.train_mse)
#tm.test_rmse <- sqrt(tm.test_mse)

# Calculate Mean Absolute Error (MAE) for training and testing
#tm.train_mae <- mean(abs(tm.train_predictions - sampled_train_data$int_rate))
#tm.test_mae <- mean(abs(tm.test_predictions - sampled_test_data$int_rate))

# Calculate R-squared (R²) for training and testing
#tm.train_r2 <- 1 - (sum((sampled_train_data$int_rate - tm.train_predictions)^2) / sum((sampled_train_data$int_rate - mean(sampled_train_data$int_rate))^2))
#tm.test_r2 <- 1 - (sum((sampled_test_data$int_rate - tm.test_predictions)^2) / sum((sampled_test_data$int_rate - mean(sampled_test_data$int_rate))^2))

# Display the metrics
#cat("Training MSE:", tm.train_mse, "\n")
#cat("Testing MSE:", tm.test_mse, "\n")
#cat("Training RMSE:", tm.train_rmse, "\n")
#cat("Testing RMSE:", tm.test_rmse, "\n")
#cat("Training MAE:", tm.train_mae, "\n")
#cat("Testing MAE:", tm.test_mae, "\n")
#cat("Training R-squared (R²):", tm.train_r2, "\n")
#cat("Testing R-squared (R²):", tm.test_r2, "\n")

#### Random Forest ####

# Train a Random Forest model
rf <- ranger(formula = int_rate ~ ., data = sampled_train_data, num.trees = 500, verbose=TRUE, importance = "impurity", oob.error = TRUE)

# Print the model summary
print("Random Forest Model Summary:")
print(rf)

# Make predictions on the training and testing data
rf.train_predictions <- predict(rf, data = sampled_train_data)
rf.test_predictions <- predict(rf, data = sampled_test_data)

# Calculate Mean Squared Error (MSE) for training and testing
rf.train_mse <- mean((rf.train_predictions$predictions - sampled_train_data$int_rate)^2)
rf.test_mse <- mean((rf.test_predictions$predictions - sampled_test_data$int_rate)^2)

# Calculate Root Mean Squared Error (RMSE) for training and testing
rf.train_rmse <- sqrt(rf.train_mse)
rf.test_rmse <- sqrt(rf.test_mse)

# Calculate Mean Absolute Error (MAE) for training and testing
rf.train_mae <- mean(abs(rf.train_predictions$predictions - sampled_train_data$int_rate))
rf.test_mae <- mean(abs(rf.test_predictions$predictions - sampled_test_data$int_rate))

# Calculate R-squared (R²) for training and testing
rf.train_r2 <- 1 - (sum((sampled_train_data$int_rate - rf.train_predictions$predictions)^2) / sum((sampled_train_data$int_rate - mean(sampled_train_data$int_rate))^2))
rf.test_r2 <- 1 - (sum((sampled_test_data$int_rate - rf.test_predictions$predictions)^2) / sum((sampled_test_data$int_rate - mean(sampled_test_data$int_rate))^2))

# Display the metrics
cat("Training MSE:", rf.train_mse, "\n")
cat("Testing MSE:", rf.test_mse, "\n")
cat("Training RMSE:", rf.train_rmse, "\n")
cat("Testing RMSE:", rf.test_rmse, "\n")
cat("Training MAE:", rf.train_mae, "\n")
cat("Testing MAE:", rf.test_mae, "\n")
cat("Training R-squared (R²):", rf.train_r2, "\n")
cat("Testing R-squared (R²):", rf.test_r2, "\n")
#rf <- randomForest(int_rate~., data=train_data, ntree = 5, mtry = 3)
#bag.boston=randomForest(medv~.,data=Boston,subset=train, mtry=13,importance =TRUE)
#print(rf)

# Set the number of cores you want to use
#num_cores <- 6  # Adjust this number based on your system's capabilities

# Register parallel backend
#cl <- makeCluster(num_cores)
#registerDoParallel(cl)

# Assuming 'lc_data' is your dataset
#rf_model <- foreach(ntree = rep(100, num_cores), .packages = 'randomForest') %dopar% {
#    randomForest(int_rate ~ ., data = lc_data, ntree = ntree, mtry = sqrt(ncol(lc_data)))
#}

# After training, stop the cluster to release the cores:
#stopCluster(cl)

#### Boosting ####

# Define the target variable for training and testing
xgb.y_train <- sampled_train_data$int_rate
xgb.y_test <- sampled_test_data$int_rate  # Use sampled_test_data for testing

# Define the feature matrix for training and testing (exclude the target variable)
xgb.X_train <- sampled_train_data[, -which(names(sampled_train_data) == 'int_rate')]
xgb.X_test <- sampled_test_data[, -which(names(sampled_test_data) == 'int_rate')]  # Use sampled_test_data for testing

# Fit a gradient boosting regression model using xgboost
xgb <- xgboost(
  data = as.matrix(xgb.X_train),
  label = xgb.y_train,
  nrounds = 100,
  verbose = 0
)

# Make predictions on the training and testing data
xgb.train_predictions <- predict(xgb, newdata = as.matrix(xgb.X_train))
xgb.test_predictions <- predict(xgb, newdata = as.matrix(xgb.X_test))

# Calculate Mean Squared Error (MSE) for training and testing
xgb.train_mse <- mean((xgb.train_predictions - xgb.y_train)^2)
xgb.test_mse <- mean((xgb.test_predictions - xgb.y_test)^2)

# Calculate Root Mean Squared Error (RMSE) for training and testing
xgb.train_rmse <- sqrt(xgb.train_mse)
xgb.test_rmse <- sqrt(xgb.test_mse)

# Calculate Mean Absolute Error (MAE) for training and testing
xgb.train_mae <- mean(abs(xgb.train_predictions - xgb.y_train))
xgb.test_mae <- mean(abs(xgb.test_predictions - xgb.y_test))

# Calculate R-squared (R²) for training and testing
xgb.train_r2 <- 1 - (sum((xgb.y_train - xgb.train_predictions)^2) / sum((xgb.y_train - mean(xgb.y_train))^2))
xgb.test_r2 <- 1 - (sum((xgb.y_test - xgb.test_predictions)^2) / sum((xgb.y_test - mean(xgb.y_test))^2))

# Display the metrics
cat("Training MSE:", xgb.train_mse, "\n")
cat("Testing MSE:", xgb.test_mse, "\n")
cat("Training RMSE:", xgb.train_rmse, "\n")
cat("Testing RMSE:", xgb.test_rmse, "\n")
cat("Training MAE:", xgb.train_mae, "\n")
cat("Testing MAE:", xgb.test_mae, "\n")
cat("Training R-squared (R²):", xgb.train_r2, "\n")
cat("Testing R-squared (R²):", xgb.test_r2, "\n")
```
Following, a scatter plot of actual vs predicted training values for each model is plot.
This plot helps us visualize how well each model's predictions align with the actual data points.
```{r}
# Create a scatter plot function
create_scatter_plot <- function(actual_values, predicted_values, model_name) {
  model_comparison_data <- data.frame(
    Actual = actual_values,
    Predicted = predicted_values
  )
  
  scatter_plot <- ggplot(model_comparison_data, aes(x = Actual, y = Predicted)) +
    geom_point() +
    geom_abline(intercept = 0, slope = 1, linetype = "dashed", color = "red") +  # Add a diagonal reference line
    labs(x = "Actual Training Values", y = "Predicted Training Values", title = model_name) +
    theme_minimal() +
    ylim(-50, 50)
  
  return(scatter_plot)
}

# Create scatter plots for each model
lm_scatter_plot <- create_scatter_plot(
  actual_values = sampled_train_data$int_rate,
  predicted_values = lm.train_predictions,
  model_name = "Linear Regression"
)

rf_scatter_plot <- create_scatter_plot(
  actual_values = sampled_train_data$int_rate,
  predicted_values = rf.train_predictions$predictions,
  model_name = "Random Forest"
)

xgb_scatter_plot <- create_scatter_plot(
  actual_values = xgb.y_train,
  predicted_values = xgb.train_predictions,
  model_name = "XGBoost"
)

# Display the scatter plots separately
print(lm_scatter_plot)
print(rf_scatter_plot)
print(xgb_scatter_plot)
```
Following, a scatter plot of actual vs predicted testing values for each model is plot.
This plot helps us visualize how well each model's predictions align with the actual data points.
```{r}
# Create a scatter plot function
create_scatter_plot <- function(actual_values, predicted_values, model_name) {
  model_comparison_data <- data.frame(
    Actual = actual_values,
    Predicted = predicted_values
  )
  
  scatter_plot <- ggplot(model_comparison_data, aes(x = Actual, y = Predicted)) +
    geom_point() +
    geom_abline(intercept = 0, slope = 1, linetype = "dashed", color = "red") +  # Add a diagonal reference line
    labs(x = "Actual Testing Values", y = "Predicted Testing Values", title = model_name) +
    theme_minimal() +
    ylim(-50, 50) +
    xlim(0, 40)
  
  return(scatter_plot)
}

# Create scatter plots for each model
lm_scatter_plot <- create_scatter_plot(
  actual_values = sampled_test_data$int_rate,
  predicted_values = lm.test_predictions,
  model_name = "Linear Regression"
)

rf_scatter_plot <- create_scatter_plot(
  actual_values = sampled_test_data$int_rate,
  predicted_values = rf.test_predictions$predictions,
  model_name = "Random Forest"
)

xgb_scatter_plot <- create_scatter_plot(
  actual_values = xgb.y_test,
  predicted_values = xgb.test_predictions,
  model_name = "XGBoost"
)

# Display the scatter plots separately
print(lm_scatter_plot)
print(rf_scatter_plot)
print(xgb_scatter_plot)
```

Residual plots can help identify patterns in prediction errors and assess whether the assumptions of linear regression (if applicable) are met.
```{r}
# Create a residual plot function
create_residual_plot <- function(actual_values, predicted_values, model_name) {
  residuals <- actual_values - predicted_values
  residual_data <- data.frame(
    Predicted = predicted_values,
    Residuals = residuals
  )
  
  residual_plot <- ggplot(residual_data, aes(x = Predicted, y = Residuals)) +
    geom_point() +
    geom_hline(yintercept = 0, linetype = "dashed", color = "red") +  # Red horizontal reference line
    labs(x = "Predicted Values", y = "Residuals", title = paste("Residual Plot -", model_name)) +
    theme_minimal() +
    ylim(-30, 30) +
    xlim(0, 40)
  
  return(residual_plot)
}

# Create residual plots for each model
lm_residual_plot <- create_residual_plot(
  actual_values = sampled_train_data$int_rate,
  predicted_values = lm.train_predictions,
  model_name = "Linear Regression"
)

rf_residual_plot <- create_residual_plot(
  actual_values = sampled_train_data$int_rate,
  predicted_values = rf.train_predictions$predictions,
  model_name = "Random Forest"
)

xgb_residual_plot <- create_residual_plot(
  actual_values = xgb.y_train,
  predicted_values = xgb.train_predictions,
  model_name = "XGBoost"
)

# Display the residual plots separately
print(lm_residual_plot)
print(rf_residual_plot)
print(xgb_residual_plot)
```
From the plots above we can clearly see that:

-   Linear Regression Residual Plot:
    -   Pattern: There appears to be a clear pattern in the residuals, with a funnel shape that widens as the predicted values increase. This suggests heteroscedasticity, where the variance of the residuals is not constant across the range of predicted values.
    -   Outliers: There are several prominent outliers, particularly for higher predicted values. These points significantly deviate from the red dashed line, which represents zero residuals.
-   Random Forest Residual Plot:
    -   Pattern: The residuals seem to be randomly dispersed around the zero line at lower predicted values, which is a good sign. However, as predicted values increase, the residuals also increase, suggesting a systematic error in the model predictions.
    -   Concentration: There is a higher concentration of residuals around the zero line compared to the Linear Regression model, which could indicate a better fit
-    XGBoost Residual Plot:
    -   Pattern: The residuals in this plot are more evenly dispersed across the predicted values than in the Linear Regression plot, suggesting a more consistent variance (homoscedasticity) and potentially a better fit.
    -   Outliers: This plot also shows outliers, but they do not appear as extreme as in the Linear Regression plot. The spread of residuals is narrower compared to the Random Forest plot.
-   Comparison:
    -   Heteroscedasticity: The Linear Regression model exhibits clear heteroscedasticity, which is a sign of model inadequacy. This could be improved with transformations or using models that handle non-constant variance better.
    -   Model Fit: The Random Forest model seems to fit the lower range of predicted values well but shows increasing residuals with higher predicted values, which could indicate overfitting or a lack of generalization for higher values.
    -   Consistency: The XGBoost model seems to show a more consistent spread of residuals around the zero line, which is indicative of a model that has a consistent performance across the range of predicted values.
    -   Outliers: All three models have outliers, but their impact seems most pronounced in the Linear Regression model.

This visualization can help you compare the distribution of prediction errors across models.
```{r}
# Create a density plot function for residuals
create_residual_density_plot <- function(actual_values, predicted_values, model_name) {
  residuals <- actual_values - predicted_values
  residual_data <- data.frame(Residuals = residuals)
  
  density_plot <- ggplot(residual_data, aes(x = Residuals)) +
    geom_density(fill = "skyblue", color = "black", alpha = 0.7) +
    labs(x = "Residuals", y = "Density", title = paste("Residual Density Plot -", model_name)) +
    theme_minimal()
  
  return(density_plot)
}

# Create density plots for residuals for each model
lm_residual_density_plot <- create_residual_density_plot(
  actual_values = sampled_train_data$int_rate,
  predicted_values = lm.train_predictions,
  model_name = "Linear Regression"
)

rf_residual_density_plot <- create_residual_density_plot(
  actual_values = sampled_train_data$int_rate,
  predicted_values = rf.train_predictions$predictions,
  model_name = "Random Forest"
)

xgb_residual_density_plot <- create_residual_density_plot(
  actual_values = xgb.y_train,
  predicted_values = xgb.train_predictions,
  model_name = "XGBoost"
)

# Display the density plots separately
print(lm_residual_density_plot)
print(rf_residual_density_plot)
print(xgb_residual_density_plot)
```

This visualization can help you compare the distribution of prediction errors across models through histograms.

```{r}
# Create a histogram plot function for residuals with a red density curve
create_residual_histogram_plot <- function(actual_values, predicted_values, model_name) {
  residuals <- actual_values - predicted_values
  residual_data <- data.frame(Residuals = residuals)
  
  histogram_plot <- ggplot(residual_data, aes(x = Residuals)) +
    geom_histogram(aes(y = after_stat(density)), bins = 30, fill = "skyblue", color = "black", alpha = 0.7) +  # Use density on the y-axis for the histogram
    geom_density(color = "red", linewidth = 1.5) +  # Add the density plot in red
    labs(x = "Residuals", y = "Density", title = paste("Residual Histogram Plot with Density Curve -", model_name)) +
    theme_minimal() +
    xlim(-20,20) + 
    ylim(0, 0.3)
  
  return(histogram_plot)
}

# Create histogram plots for residuals for each model
lm_residual_histogram_plot <- create_residual_histogram_plot(
  actual_values = sampled_train_data$int_rate,
  predicted_values = lm.train_predictions,
  model_name = "Linear Regression"
)

rf_residual_histogram_plot <- create_residual_histogram_plot(
  actual_values = sampled_train_data$int_rate,
  predicted_values = rf.train_predictions$predictions,
  model_name = "Random Forest"
)

xgb_residual_histogram_plot <- create_residual_histogram_plot(
  actual_values = xgb.y_train,
  predicted_values = xgb.train_predictions,
  model_name = "XGBoost"
)

# Display the histogram plots separately
print(lm_residual_histogram_plot)
print(rf_residual_histogram_plot)
print(xgb_residual_histogram_plot)
```

For each model a bar chart that displays the R-squared (coefficient of determination) values is created.
R-squared measures the proportion of variance in the target variable explained by the model. Higher R-squared values indicate better model fit.
```{r}
# Create a data frame with R-squared values for each model
model_names <- c("Linear Regression", "Random Forest", "XGBoost")
r_squared_values <- c(
  lm.train_r2,
  rf.train_r2,
  xgb.train_r2
)

r_squared_data <- data.frame(Model = factor(model_names),
                              R_squared = r_squared_values)

# Create the R-squared comparison bar chart
r_squared_bar_chart <- ggplot(r_squared_data, aes(x = Model, y = R_squared, fill = Model)) +
  geom_bar(stat = "identity") +
  labs(x = "Model", y = "R-squared (R²)", title = "R-squared Comparison") +
  theme_minimal() +
  theme(axis.text.x = element_text(angle = 45, hjust = 1))

# Display the R-squared comparison bar chart
print(r_squared_bar_chart)
```
A bar chart that compares the MAE or RMSE values, is generated for each model.
These metrics quantify the average prediction errors of each model, and lower values are preferred.
```{r}
# Create a data frame with MAE and RMSE values for each model
model_names <- c("Linear Regression", "Random Forest", "XGBoost","Linear Regression", "Random Forest", "XGBoost")
error_values_train <- c(
  lm.train_mae,
  rf.train_mae,
  xgb.train_mae,
  lm.train_rmse,
  rf.train_rmse,
  xgb.train_rmse
)
error_values_test <- c(
  lm.test_mae,
  rf.test_mae,
  xgb.test_mae,
  lm.test_rmse,
  rf.test_rmse,
  xgb.test_rmse
)
error_type <- c(
  "MAE", "MAE", "MAE","RMSE","RMSE","RMSE"
)
model_errors_train <- data.frame(Model = factor(model_names, levels = c("Linear Regression", "Random Forest", "XGBoost")),
                Error = error_values_train, Type = error_type)
model_errors_test <- data.frame(Model = factor(model_names, levels = c("Linear Regression", "Random Forest", "XGBoost")),
                Error = error_values_test, Type = error_type)
# Create the MAE or RMSE comparison bar chart
error_bar_chart_train <- ggplot(model_errors_train, aes(x = Model, y = Error, fill = Type)) +
  geom_bar(stat = "identity", position = "dodge") +
  labs(x = "Model", y = "Error Value", title = "Training MAE and RMSE Comparison") +
  theme_minimal() +
  theme(axis.text.x = element_text(angle = 45, hjust = 1)) + 
  ylim(0, 4)

error_bar_chart_test <- ggplot(model_errors_test, aes(x = Model, y = Error, fill = Type)) +
  geom_bar(stat = "identity", position = "dodge") +
  labs(x = "Model", y = "Error Value", title = "Testing MAE and RMSE Comparison") +
  theme_minimal() +
  theme(axis.text.x = element_text(angle = 45, hjust = 1)) + 
  ylim(0, 4)

# Display the MAE and RMSE comparison bar chart
print(error_bar_chart_train)
print(error_bar_chart_test)
```


```{r}
#### Random Forest Feature Importance Plot ####
v1 <- vip(rf, title = "Ranger", num_features = 20) 
plot(v1)
```


Learning curve using RMSE and R^2:
```{r}
# TODO: change the x-axes
# Create a data frame with RMSE and R-squared values for each model and sample size
model_names <- c("Linear Regression", "Random Forest", "XGBoost")
sample_sizes <- seq(10, nrow(sampled_train_data), by = 10)  # Adjust the sample sizes as needed

# Create data frames with RMSE and R-squared values for each model
rmse_data <- data.frame(
  Model = rep(model_names, each = length(sample_sizes)),
  Sample_Size = rep(sample_sizes, times = length(model_names)),
  RMSE = c(
    lm.train_rmse, rf.train_rmse, xgb.train_rmse
  )
)

r_squared_data <- data.frame(
  Model = rep(model_names, each = length(sample_sizes)),
  Sample_Size = rep(sample_sizes, times = length(model_names)),
  R_squared = c(
    lm.train_r2, rf.train_r2, xgb.train_r2
  )
)

# Create RMSE learning curve
rmse_curve <- ggplot(rmse_data, aes(x = Sample_Size, y = RMSE, color = Model)) +
  geom_line() +
  labs(x = "Sample Size", y = "RMSE", title = "RMSE Learning Curve") +
  theme_minimal()

# Create R-squared learning curve
r_squared_curve <- ggplot(r_squared_data, aes(x = Sample_Size, y = R_squared, color = Model)) +
  geom_line() +
  labs(x = "Sample Size", y = "R-squared", title = "R-squared Learning Curve") +
  theme_minimal()

# Display the RMSE and R-squared learning curves
print(rmse_curve)
print(r_squared_curve)
```



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